The quantizing effect of potentials on the critical number of reaction-diffusion equations

DOI10.1006/jdeq.2000.3815zbMath0973.35035OpenAlexW1986185035MaRDI QIDQ5929882

Qi S. Zhang

Publication date: 15 November 2001

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

Full work available at URL: https://doi.org/10.1006/jdeq.2000.3815

zbMATH Keywords

semilinear heat equationFujita's critical exponentglobal estimates of Schrödinger heat kernelsLiouville theorem for semilinear elliptic equations

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Reaction-diffusion equations (35K57) Critical exponents in context of PDEs (35B33)

Related Items (8)

On the Fujita exponent for a semilinear heat equation with a potential term ⋮ Global positive solution to a semi-linear parabolic equation with potential on Riemannian manifold ⋮ Large time behaviors of hot spots for the heat equation with a potential ⋮ Existence and nonexistence results for higher-order semilinear evolution inequalities with critical potential ⋮ Large time behavior of reaction-diffusion equations with Bessel generators ⋮ The Fujita exponent for semilinear heat equations with quadratically decaying potential or in an exterior domain ⋮ Nonexistence results for parabolic equations involving the \(p\)-Laplacian and Hardy-Leray-type inequalities on Riemannian manifolds ⋮ Existence and nonexistence results for reaction-diffusion equations in product of cones

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