Structure of the set of steady-state solutions and asymptotic behavior of semilinear heat equations

From MaRDI portal
Publication:1167346

DOI10.1016/0022-0396(84)90031-7zbMath0491.35057OpenAlexW2084966183MaRDI QIDQ1167346

Pierre-Louis Lions

Publication date: 1984

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(84)90031-7




Related Items (27)

Stabilization of arbitrary structures in a doubly degenerate reaction-diffusion system modeling bacterial motion on a nutrient-poor agarCONVERGENCE TO EQUILIBRIUM FOR SEMILINEAR PARABOLIC PROBLEMS INEventual monotonicity and convergence to travelling fronts for the solutions of parabolic equations in cylindersA simple unified approach to some convergence theorems of L. SimonConvergence to steady states in asymptotically autonomous semilinear evolution equations.Existence, multiplicity, shape and attractivity of heterogeneous steady states for bistable reaction-diffusion equations in the planeAsymptotic behavior of an adapted implicit discretization of slowly damped second order dynamical systemsGlobal existence and finite time blowup for a nonlocal semilinear pseudo-parabolic equationAsymptotic behavior and decay rate estimates for a class of semilinear evolution equations of mixed orderControl under constraints for multi-dimensional reaction-diffusion monostable and bistable equationsWell-posedness and qualitative properties of a dynamical model for the ideal free distributionDoes spatial homogeneity ultimately prevail in nutrient taxis systems? A paradigm for structure support by rapid diffusion decay in an autonomous parabolic flowLinearized stability for degenerate and singular semilinear and quasilinear parabolic problems: the linearized singular equationEstimations C1 pour des problèmes paraboliques semi-linéairesOn the stability of initial conditions for the parabolic Gelfand problemConvergence in gradient-like systems which are asymptotically autonomous and analyticGlobal attractors and convergence to equilibrium for degenerate Ginzburg-Landau and parabolic equationsNon-genericity of initial data with punctual \(\omega \)-limit setAsymptotic stability criterion for nonlinear monotonic systems and its applications (review)A threshold phenomenon in the propagation of a point source initiated flameConvergence of global and bounded solutions of the wave equation with linear dissipation and analytic nonlinearityStabilization for degenerate diffusion with absorptionConvergence in smooth strongly monotone flows defined by semilinear parabolic equationsOn the role of diffusivity in some stable equilibria of a diffusion equationControl of reaction-diffusion models in biology and social sciencesThe principle of linearized stability of a class of degenerate diffusion equationsNonconvergent bounded solutions of semilinear heat equations on arbitrary domains



Cites Work


This page was built for publication: Structure of the set of steady-state solutions and asymptotic behavior of semilinear heat equations