Upper and lower solutions for a homogeneous Dirichlet problem with nonlinear diffusion and the principle of linearized stability

DOI10.1216/rmjm/1021477348zbMath1002.35017OpenAlexW1981179256MaRDI QIDQ5940631

Robert Stephen Cantrell, Chris Cosner

Publication date: 12 August 2001

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/VOL30-4/CONT30-4/CONT30-4.html

zbMATH Keywords

quasilinear parabolic problems

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Stability in context of PDEs (35B35)

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Eigenvalue problems of a degenerate quasilinear elliptic equation ⋮ Linearized stability implies dynamic stability for equilibria of 1-dimensional, p-Laplacian boundary value problems

Cites Work

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• Dynamic theory of quasilinear parabolic systems. III: Global existence
• Diffusive Logistic Equations with Indefinite Weights: Population Models in Disrupted Environments II
• The principle of linearized stability for quasilinear parabolic evolution equations
• Dynamic theory of quasilinear parabolic equations—I. Abstract evolution equations
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
• Conditional persistence in logistic models via nonlinear diffusion
• Analytic semigroups and optimal regularity in parabolic problems

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