On bounded radial solutions
of parabolic equations on R^N: Part II--convergence
for initial data with a linearly stable limit at
infinity, Sao Paulo J. Math. Sci., to appear. Abstract Preprint.pdf |
On bounded radial solutions
of parabolic equations on R^N: Quasiconvergence for
initial data with a stable limit at infinity, Discrete
Contin. Dyn. Syst. Ser. S, 17 (2024), 1573–1587. Abstract Preprint.pdf |
Nonexistence of radial
time-periodic solutions of reaction-diffusion
equations with generic nonlinearities, J.
Differential Equations 363 (2023), 307–326. Abstract Preprint.pdf |
with A. Pauthier, Large-time behavior
of solutions of parabolic equations on the real line with
convergent initial data III: unstable limit at infinity,
Partial Differ. Equ. Appl., 3 (2022),
Paper No. 48. Abstract Preprint.pdf |
with D. Valdebenito, Further results
on quasiperiodic partially localized solutions of
homogeneous elliptic equations on R^{N+1}, J. Funct. Anal.
282 (2022), 10945. Abstract Preprint.pdf |
with D. Valdebenito, The existence of
partially localized periodic-quasiperiodic solutions and
related KAM-type results for elliptic equations on the
entire space, J. Dynam. Differential
Equations 34 (2022), 3035-3056. Abstract Preprint.pdf A correction |
with A. Pauthier, Large-time behavior
of solutions of parabolic equations on the real line with
convergent initial data II: equal limits at infinity, J.
Math. Pures Appl. 153 (2021), 137–186. Abstract Preprint.pdf |
with P. Quittner, Entire and ancient
solutions of a supercritical semilinear heat equation, Discrete
Cont. Dynamical Syst. 41 (2021), 413–438
Abstract Preprint.pdf |
with H. Matano, Dynamics of
nonnegative solutions of one-dimensional
reaction-diffusion equations with localized initial data.
Part II: Generic nonlinearities, Comm. Partial
Differential Equations 45 (2020), 483–524
Abstract Preprint.pdf |
with P. Quittner, On the multiplicity
of self-similar solutions of the semilinear heat equation,
Nonlinear Anal. 191 (2020), 111639 Abstract Preprint.pdf |
with D. Valdebenito, Existence of
partially localized quasiperiodic solutions of homogeneous
elliptic equations on R^(N+1), Annali Scuola Norm. Sup.
Pisa XXI (2020), 771-800 Abstract Preprint.pdf |
Entire solutions and a Liouville
theorem for a class of parabolic equations on the real
line, Proc. Amer. Math. Soc. 148 (2020), 2997–3008
Abstract Preprint.pdf |
with D. Valdebenito, Existence
of quasiperiodic solutions of elliptic equations on the
entire space with a quadratic nonlinearity, Discrete Cont.
Dynamical Syst., Ser. S, 13 (2020), 1369–1393 Abstract Preprint.pdf |
Propagating terraces and the dynamics
of front-like solutions of reaction-diffusion equations on
R, Mem. Amer. Math. Soc. 264 (2020), no.
1278, ISBN: 978-1-4704-4112-8; 978-1-4704-5806-5 Abstract Preprint.pdf |
with D. Valdebenito, Some generic
properties of Schrodinger operators with radial
potentials, Proc. Royal Soc.
Edinburgh 149A (2019), 1435–1451
Abstract Preprint.pdf |
with A. Pauthier, Large-time behavior
of solutions of parabolic equations on the real line with
convergent initial data, Nonlinearity 31
(2018), 4423–4441 Abstract Preprint.pdf |
with D. Valdebenito, Existence of
quasiperiodic solutions of elliptic equations on
R^{N+1} via center manifold and KAM theorems, J.
Differential Equations 262 (2017), 6109–6164 Abstract Preprint.pdf |
Convergence and quasiconvergence
properties of solutions of parabolic equations on the real
line: an overview. In
"Patterns of Dynamics,"
pp. 172–183,
Springer Proc. Math. Stat. 205, Springer, Cham, 2017
Abstract Preprint.pdf |
Planar propagating terraces and the asymptotic
one-dimensional symmetry of solutions of semilinear
parabolic equations, SIAM J. Math. Anal. 49
(2017), 3716–3740 Abstract Preprint.pdf |
with H. Matano, An entire solution of a bistable
parabolic equation on R with two colliding pulses, J.
Funct. Anal. 272 (2017), 1956-1979 Abstract Preprint.pdf |
Propagating terraces in a proof of the Gibbons
conjecture and related results, J. Fixed Point Theory
Appl. 19 (2017), 113–128
Abstract Preprint.pdf |
with H. Matano, Dynamics of nonnegative solutions
of one-dimensional reaction-diffusion equations with
localized initial data. Part I: A general quasiconvergence
theorem and its consequences, Comm. Partial Differential
Equations 41 (2016),
785–811 Abstract Preprint.pdf |
Threshold behavior and non-quasiconvergent
solutions with localized initial data for bistable
reaction-diffusion equations, J. Dynam. Differential
Equations 28 (2016), 605–625 Abstract Preprint.pdf |
Spatial trajectories and convergence to traveling
fronts for bistable reaction-diffusion equations, In
Contributions to nonlinear elliptic equations and systems.
A tribute to Djairo Guedes de Figueiredo on the occasion
of his 80th Birthday, A.N. Carvalho et al. (eds), Springer
2015, 404-423 Abstract Preprint.pdf |
Examples of bounded solutions with nonstationary
limit profiles for semilinear heat equations on R, J.
Evol. Equ. 15 (2015), 281–307 Abstract Preprint.pdf |
with J. Foldes, Equilibria with a nontrivial nodal
set and the dynamics of parabolic equations on symmetric
domains, J. Differential Equations 258 (2015), 1859-1888. Abstract Preprint.pdf |
with Y. Du, Locally uniform convergence to an
equilibrium for nonlinear parabolic equations on R^N,
Indiana Univ. Math. J. 64 (2015), 787–824 Abstract Preprint.pdf |
with E. Yanagida, Localized solutions of a
semilinear parabolic equation with a recurrent
nonstationary asymptotics, SIAM J. Math. Analysis 46
(2014), 3481–3496 Abstract Preprint.pdf |
with E. Yanagida, Global unbounded solutions of the
Fujita equation in the intermediate range, Math. Ann. 360
(2014), 255–266 Abstract Preprint.pdf |
On the multiplicity of nonnegative solutions with a
nontrivial nodal set for elliptic equations on symmetric
domains, Discrete Cont. Dynam. Syst. 34 (2014), 2657–2667
Abstract Preprint.pdf |
with S. Terracini, Nonnegative solutions with a
nontrivial nodal set for elliptic equations on smooth
symmetric domains, Proc. Amer. Math. Soc. 142 (2014),
1249–1259 Abstract Preprint.pdf |
A discussion of nonnegative solutions of elliptic
equations on symmetric domains, Nonlinear Partial
Differential Equations, Dynamical Systems and Their
Applications (M. Taniguchi, ed.), RIMS Kokyuroku, vol.
1881, Kyoto University, 2014, pp. 92-106 Abstract Preprint.pdf |
Positivity and symmetry of nonnegative solutions of
semilinear elliptic equations on planar domains, J. Funct.
Anal. 262 (2012), 4458–4474
Abstract Preprint.pdf |
with J. Foldes, On asymptotically symmetric
parabolic equations, Networks and Heterogeneous Media 7
(2012), 673–689 Abstract Preprint.pdf |
with Y. Du and R. Peng, The parabolic logistic
equation with blow-up initial and boundary values, J.
Anal. Math. 118 (2012), 297–316 Abstract Preprint.pdf |
On symmetry of nonnegative solutions of elliptic
equations. Ann. Inst. H. Poincare Anal. Non Lineaire 29
(2012), 1-19 Abstract Preprint.pdf |
with J. Foldes, Convergence to a steady state for
asymptotically autonomous semilinear heat equations on
R^N. J. Differential Equations 251 (2011), 1903–1922 Abstract Preprint.pdf |
Symmetry of nonnegative solutions of elliptic
equations via a result of Serrin. Comm. Partial
Differential Equations 36 (2011), 657-669 Abstract Preprint.pdf |
Threshold solutions and sharp transitions for
nonautonomous parabolic equations on R^N. Arch. Rational
Mech. Anal. 199 (2011), 69-97 Abstract Preprint.pdf Addendum.pdf |
with T. Bartsch and P. Quittner, Liouville-type
theorems and asymptotic behavior of nodal radial solutions
of semilinear heat equations. J. European Math. Soc. 13
(2011), 219–247 Abstract Preprint.pdf |
with J. Foldes, On cooperative parabolic systems:
Harnack inequalities and asymptotic symmetry. Discrete
Cont. Dynamical Systems 21 (2009), 329–341 Abstract Preprint.pdf |
Symmetry
properties of positive solutions of parabolic equations: a
survey. In Recent Progress on Reaction-Diffusion Systems
and Viscosity Solutions, Y. Du et al. (eds), World
Scientific 2009, 170–208
Abstract Preprint.pdf |
with E.
Yanagida, Convergence of anisotropically decaying
solutions of a supercritical semilinear heat equation. J.
Dynam. Differential Equations 21 (2009), 329–341 Abstract Preprint.pdf |
with P. Quittner, Asymptotic behavior of threshold
and sub-threshold solutions of a semilinear heat equation.
Asymptot. Anal., 57 (2008), 125–141 Abstract Preprint.pdf |
with V. Sverak, Zeros of complex caloric functions
and singularities of complex viscous Burgers equation. J.
reine angew. Math. 616 (2008), 205–217 Abstract Preprint.pdf |
with J.
Huska, Exponential separation and principal Floquet
bundles for linear parabolic equations on R^N. Discrete
Cont. Dynamical Systems 20 (2008), 81–113 Abstract Preprint.pdf |
with J. Huska and M. V. Safonov, Harnack
inequalities, exponential separation, and perturbations of
principal Floquet bundles for linear parabolic equations.
Ann. Inst. H. Poincare Anal. Non Lineaire 24 (2007),
711-739 Abstract Preprint.pdf |
with P. Quittner and P. Souplet, Singularity and
decay estimates in superlinear problems via Liouville-type
theorems. Part II: Parabolic equations, Indiana Univ.
Math. J. 56 (2007), 879-908. Abstract Preprint.pdf |
with P. Quittner and P. Souplet, Singularity and
decay estimates in superlinear problems via Liouville-type
theorems. Part I: Elliptic equations and systems. Duke
Math. J. 139 (2007), 555–579
Abstract Preprint.pdf |
Estimates of solutions and asymptotic symmetry for
parabolic equations on bounded domains. Arch. Rational
Mech. Anal. 183 (2007), 59–91
Abstract Preprint.pdf Addendum.pdf |
with Y. Lou and S. Martinez, Loops and branches of
coexistence states in a Lotka-Volterra competition model.
J. Differential Equations, J. Differential Equations 230
(2006), 720–742 Abstract Preprint.pdf |
Symmetry properties of positive solutions of
parabolic equations on $R^N$: II. Entire solutions. Comm.
Partial Differential Equations 31 (2006): 1615-1638 Abstract Preprint.pdf |
with P. Quittner, A Liouville-type theorem and the
decay of radial solutions of a semilinear heat equation.
Nonlinear Analysis, TMA 64 (2006), 1679-1689 Abstract Preprint.pdf |
Symmetry properties of positive solutions of
parabolic equations on $R^N$: I. Asymptotic symmetry for
the Cauchy problem, Comm. Partial Differential Equations
30 (2005), 1567-1593 Abstract Preprint.pdf |
with J. Huska and M.V. Safonov, Principal
eigenvalues, spectral gaps and exponential separation
between positive and sign-changing solutions of parabolic
equations, Proceedings of the 5th International Conference
on Dynamical Systems and Differential Equations, Pomona
2004. Disc. Cont. Dynamical Systems, Supplement 2005, pp.
427-435 Abstract |
with M. Fila and H. Matano, Immediate
regularization after blow-up. SIAM J. Math. Analysis 37
(2005), 752-776 Abstract |
with P. Quittner, Liouville-type theorems and
complete blow-up for indefinite superlinear parabolic
equations, In Nonlinear Elliptic and
Parabolic Problems, M. Chipot and J. Escher (eds.),
Progress in Nonlinear Differential Equations and Their
Applications, Vol. 64, Birkhauser,
Basel, 2005, 391-402
Abstract |
Asymptotic symmetry of positive solutions of
parabolic equations, Proceedings of Equadiff 2003,
F. Dumortier et al. (eds), World Scientific 2005, 99-108 Abstract |
with M. Fila and H. Matano, Immediate
regularization after blow-up. Proceedings of Equadiff 2003,
F. Dumortier et al. (eds), World Scientific 2005, 284-289. Abstract |
with E. Yanagida, A Liouville property and
quasiconvergence for a semilinear heat equation. J.
Differential Equations, 208 (2005), 194-214. Abstract |
On uniqueness of positive entire solutions and
other properties of linear parabolic equations. Discrete
Contin. Dynamical Systems, 12 (2005), 13-26. Abstract |
with J. Huska, The principal Floquet bundle and
exponential separation for linear parabolic equations. J.
Dynam. Differential Equations, 16 (2004), 347-375. Abstract |
with E. Yanagida, Nonstabilizing solutions and
grow-up set for a supercritical semilinear diffusion
equation. Differential Integral Equations, 17 (2004),
535-548. Abstract |
with M.-A. Jendoubi, Nonstabilizing solutions of
semilinear hyperbolic and elliptic equations with damping.
Proc. Royal Soc. Edinburgh 133A (2003), 1137-1153. Abstract |
with E. Yanagida, On bounded and unbounded global
solutions of a supercritical semilinear heat equation.
Math. Ann. 327 (2003), 745-771. Abstract |
with V. Hutson, Y. Lou and K. Mischaikow, Competing
species near a degenerate limit. SIAM J. Math. Analysis 35
(2003), 453-491. Abstract |
On $L^1$-heteroclinic solutions of a semilinear
parabolic equation, Proceedings of the Conference on
Nonlinear Partial Differential Equations: Diffusion,
Cross-diffusion and Related Topics", Ryukoku 2002; Y.
Morita et al. (eds.), Ryukoku University, Ryukoku 2003,
pp. 62-68. Abstract |
with J. Busca and M.-A. Jendoubi, Convergence to
equilibrium for semilinear parabolic problems in $\R^N$.
Comm. Partial Differential Equations 27 (2002), 1793-1814. Abstract |
with F. Simondon,
Nonconvergent bounded
solutions of semilinear heat equations on arbitrary
domains, J. Differential Equations 186 (2002),
586-610. Abstract |
Some common asymptotic properties of semilinear
parabolic, hyperbolic and elliptic equations, Proc. Equadiff 10,
Math. Bohemica 127 (2002), 301-310. Abstract |
with M. Fila and H. Matano, Existence of
$L^1$-connections between equilibria of a semilinear
parabolic equation. J. Dynam. Differential Equations 14
(2002), 463-491. Abstract |
Parabolic equations: asymptotic behavior and
dynamics on invariant manifolds (survey). Handbook
on Dynamical Systems vol. 2, B.
Fiedler (ed.), Elsevier, Amsterdam 2002, pp. 835-883. Abstract |
with E. Yanagida,
Stable subharmonic
solutions of reaction-diffusion equations on an
arbitrary domain. Discrete Contin.
Dynam. Systems 8 (2002), 209-218. Abstract |
with V. Hutson and K. Mischaikow, The evolution of
dispersal rates in a heterogeneous time-periodic
environment. J. Math. Biology 43 (2001), 501-533. Abstract |
Morse indices and bifurcations of positive
solutions of $\Delta u+f(u)=0$ on $R^N$. Indiana Univ.
Math. J. 50 (2001), 1407-1432. Abstract |
with W.-M. Ni and E. Yanagida, Monotonicity of
stable solutions in shadow systems. Trans. Amer. Math.
Soc. 353 (2001), 5057-5069. Abstract |
with E. Yanagida, Existence of stable subharmonic
solutions for reaction-diffusion equations, J.
Differential Equations 169 (2001), 255-280. Abstract |
Stable subharmonic solutions of reaction-diffusion
equations, Proc. of Equadiff
99 , B. Fiedler, K. Groger, J.
Sprekels (eds), World Scientific, Singapore, 2000, pp.
722-725. Abstract |
with E. Yanagida, Stable subharmonic solutions and
asymptotic behavior in reaction-diffusion equations, E. J.
Qualitative Theory Diff. Equations 2000: Proc. 6th
Colloquium on Qualitative Properties
of Differential Equations No. 22. (2000), pp. 1-10. Abstract |
with E. Feireisl, Structure of periodic solutions
and asymptotic behavior for time- periodic
reaction-diffusion equations on R, Adv. Differential
Equations 5 (2000), 583-622. Abstract |
On the dynamics of scalar parabolic equations, in:
New Trends in Nonlinear Partial Differential Equations, Y.
Morita et al. (eds.), Ryukoku University, Ryukoku 2000,
pp. 32-45. Abstract |
with M. Fila, Global nonexistence without blow-up
for an evolution problem, Math. Zeitschrift 232 (1999),
531-545. Abstract |
Persistent saddle-connection in a class
of reaction-diffusion equations, J.
Differential Equations 156 (1999), 182-210. Abstract |
with M. Fila, Global solutions of a
semilinear parabolic equation,
Adv. Differential Equations 4 (1999),
163-196. Abstract |
with E. N. Dancer, Realization of vector
fields and dynamics of spatially
homogeneous parabolic equations, Mem.
Amer. Math. Soc. 140 (1999), viii+82. Abstract |
with P. Brunovsky, Morse-Smale structure of
a generic reaction diffusion equation in higher
space dimension, J. Differential Equations.
135 (1997), 129-181. Abstract |
Reaction-diffusion equations and realization of
gradient vector fields, Proc. EQUADIFF 95,
L. Magalhaes, C. Rocha and L. Sanchez (eds.),
World Scientific, Singapore 1998, 197-206. Abstract |
with P. Brunovsky, On the local
structure of $\omega$-limit sets of maps, J. Appl. Math.
Physics (ZAMP) 48 (1997), 976-986. Abstract with X.-Y. Chen, Asymptotic periodicity of
positive solutions of reaction-diffusion equations on
a ball, J. reine angew. Math. 472 (1996), 17-51. |
with V. Sosovicka, Stable periodic
solutions of a spatially homogeneous nonlocal
reaction-diffusion equation, Proc. Royal Soc.
Edinburgh 126A (1996), 867-884. Abstract |
with K. P. Rybakowski,
Nonconvergent bounded trajectories in semilinear heat
equations, J. Differential Equations., 124
(1996), 472-494. Abstract |
with K. P. Rybakowski, Imbedding vector
fields into Dirichlet BVPs, Annali Scuola Norm.
Sup. Pisa XXI (1995), 737-749. Abstract |
Realization of dynamics of ODE's in scalar
parabolic PDE's, Equadiff 8, Bratislava 1993,
Tatra Mountains Math. Publ. 4 (1994), pp. 179-185. Abstract |
Transversal and nontransversal intersection of
stable and unstable manifolds of
reaction-diffusion equations on symmetric
domains, Differential Integral Equations 7 (1994),
1527-1545. Abstract |
with X.-Y. Chen, Gradient-like structure
and Morse decompositions for time periodic
one-dimensional parabolic equations, J. Dynam.
Differential Equations. 7 (1995), 73-107. Abstract |
with P. Hess, Symmetry and convergence
properties for nonnegative solutions of
nonautonomous reaction- diffusion
problems, Proc. Royal Soc. Edinburgh 124A (1994),
573-587. Abstract |
with A. Haraux, Convergence to a positive
equilibrium for some nonlinear evolution equations, Acta
Math. Univ. Comenianae, LXI (1992), 129-141 Abstract |
High-dimensional $\omega$-limit sets and chaos in
scalar parabolic equations, J. Differential
Equations. 119 (1995), 24-53 Abstract |
Dynamics of scalar parabolic equations, in: Proc. Equadiff 1991, C. Perell\'o, C. Sim\'o, J. Sola-Morales (eds.), World Scientific, London 1993, pp 215-224 |
with I. Terescak, Exponential separation
and invariant bundles for maps in ordered Banach
spaces with applications to parabolic
equations, J. Dynam. Differential Equations. 5
(1993), 279-303. Abstract |
with P. Hess, Boundedness of prime periods
of stable cycles and convergence to fixed points in
discrete monotone dynamical systems, SIAM J. Math.
Anal. 24 (1993), 1312-1330 Abstract |
with P. Brunovsky, X. Mora and J. Sola-Morales, Asymptotic behavior of semilinear elliptic equations on an unbounded strip, Acta. Math. Univ. Comenianae LX (1991), 163-183 |
with. I. Terescak, Convergence to cycles as a
typical asymptotic behavior in smooth
strongly monotone discrete-time dynamical
systems, Arch. Rational Mech. Anal. 116 (1991),
339-360. Abstract |
Realization of any finite jet in a scalar semilinear parabolic equation on the ball in $R^3$, Ann. Scuola Norm. Sup. Pisa, XVIII (1991), 83-102 |
Imbedding of any vector field in a scalar
semilinear parabolic equations, Proc. Amer. Math.
Soc. 115 (1992), 1001-1008. Abstract |
with P. Brunovsky and B. Sandstede, Convergence
in general periodic parabolic equations in one
space dimension, Nonlinear Analysis, TMA, 18
(1992), 209-215 Abstract |
Complicated dynamics in scalar semilinear parabolic equations in higher space dimension, J. Differential Equations 89 (1991), 244-271 |
Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows, Comm. Math. Univ. Carolinae 31 (1990), 263-276 |
with B. Fiedler, Complicated dynamics of scalar reaction diffusion equations with a nonlocal term, Proc. Royal Soc. Edinburgh, 115 (1990), 263-276. |
Domains of attraction of equilibria and monotonicity properties of convergent trajectories in parabolic systems admitting strong comparison principle, J. reine angew. Math. 400 (1989), 32-56. |
Generic properties of strongly monotone semiflows defined by ordinary and parabolic differential equations, in: Colloquia Mathematica Soc. J. Bolyai 53, North-Holland, Budapest 1990, pp. 519-530. |
Convergence in smooth strongly monotone flows defined by semilinear parabolic equations, J. Differential Equations 79 (1989), 89-110. |
with J. Mierczynski, Group actions on strongly monotone dynamical systems, Math. Ann. 283 (1989), 1-11. |
with P. Brunovsk\'y, Generic hyperbolicity for reaction-diffusion equations on symmetric domains, J. Applied Math. Physics (ZAMP) 38 (1987), 172-183. |
Generic hyperbolicity in one-dimensional reaction-diffusion equation with general boundary conditions, Nonlinear Analysis, TMA, 11 (1987), 593-597. |