Global Behavior for a Class of Nonlinear Evolution Equations

DOI10.1137/0516018zbMath0572.35062OpenAlexW2036706294MaRDI QIDQ3689572

Paul E. Sacks

Publication date: 1985

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0516018

zbMATH Keywords

decay estimateslarge time behavioursuper and subsolutionsglobal behaviorpositive steady stateComparison methodsporous media with absorption

Mathematics Subject Classification ID

Related Items (36)

Blow-up for degenerate nonlinear parabolic problem ⋮ Behavior Near t=0 for Solutions of the Dirichlet Problem foru(t)= δφ(u)−f(u)in Bounded Domains ⋮ Global behaviour of solutions to some nonlinear diffusion equations ⋮ Global existence and nonexistence for degenerate parabolic systems ⋮ B-Methods for the Numerical Solution of Evolution Problems with Blow-Up Solutions Part I: Variation of the Constant ⋮ Global solutions for some nonlinear parabolic equations with nonmonotonic perturbations ⋮ L∞-estimates of solutions of some nonlinear degenerate parabolic equations ⋮ Blow-up for a degenerate reaction-diffusion system with nonlinear nonlocal sources ⋮ The Liouville theorem of a torsion system and its application to symmetry group of a porous medium type equation on symmetric spaces ⋮ Properties of solutions to porous medium problems with different sources and boundary conditions ⋮ Nonlocal nonlinear diffusion equations. Smoothing effects, Green functions, and functional inequalities ⋮ On the existence and regularity of solutions to singular parabolic \(p\)-Laplacian equations with absorption term ⋮ Doubly nonlinear parabolic equations with measure data ⋮ Blow-up for a degenerate parabolic equation with a nonlocal source. ⋮ A quasilinar heat equation with a source: Peaking, localization, symmetry exact solutions, asymptotics, structures ⋮ Blow-up and global existence for the porous medium equation with reaction on a class of Cartan-Hadamard manifolds ⋮ Initial blow-up rates and universal bounds for nonlinear heat equations. ⋮ Regional blow-up of solutions to the initial boundary value problem foru_t=u^δ(Δu +u) ⋮ Blow-up for a degenerate parabolic equation with a nonlocal source ⋮ BLOWUP FOR A DEGENERATE AND SINGULAR PARABOLIC EQUATION WITH NON-LOCAL SOURCE AND ABSORPTION ⋮ Blow-up and global existence for solutions to the porous medium equation with reaction and fast decaying density ⋮ Numerical solution of a Cauchy problem for nonlinear reaction diffusion processes ⋮ Numerical solution of a nonlinear reaction diffusion equation ⋮ Smoothing effects and infinite time blowup for reaction-diffusion equations: an approach via Sobolev and Poincaré inequalities ⋮ Global existence of solutions and smoothing effects for classes of reaction-diffusion equations on manifolds ⋮ Singular reaction diffusion equations of porous medium type ⋮ A positivity preserving finite element-finite volume solver for the Spalart-Allmaras turbulence model ⋮ Unnamed Item ⋮ Blow-up and global existence for solutions to the porous medium equation with reaction and slowly decaying density ⋮ Numerical solution of fast diffusion or slow diffusion equations ⋮ A degenerate diffusion equation with a nonlinear source term ⋮ On the asymptotic behavior of solutions of certain quasilinear parabolic equations ⋮ Stabilization criteria for thermally explosive materials ⋮ The principle of linearized stability of a class of degenerate diffusion equations ⋮ Existence and decay of global solutions of some nonlinear degenerate parabolic equations ⋮ Blow-up and global existence for a nonlocal degenerate parabolic system

This page was built for publication: Global Behavior for a Class of Nonlinear Evolution Equations