On the Fujita exponent for a semilinear heat equation with a potential term

DOI10.1016/j.jmaa.2008.02.059zbMath1152.35051OpenAlexW2058963363MaRDI QIDQ2427760

Kazuhiro Ishige

Publication date: 28 May 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.02.059

zbMATH Keywords

blow-upglobal existenceFujita exponent

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Critical exponents in context of PDEs (35B33) Initial value problems for second-order parabolic equations (35K15)

Related Items (11)

Existence and nonexistence of global solutions for a semilinear reaction-diffusion system ⋮ Global nonexistence of solutions for Caputo fractional differential inequality with singular potential term ⋮ Critical dissipative estimate for a heat semigroup with a quadratic singular potential and critical exponent for nonlinear heat equations ⋮ On the absence of weak solutions of nonlinear nonnegative higher order parabolic inequalities with a nonlocal source ⋮ Global positive solution to a semi-linear parabolic equation with potential on Riemannian manifold ⋮ Critical exponent for a quasilinear parabolic equation with inhomogeneous density in a cone ⋮ The critical Fujita exponent for a diffusion equation with a potential term ⋮ Global existence of solutions for the heat equation with a nonlinear boundary condition ⋮ Global existence of solutions to a weakly coupled critical parabolic system in two-dimensional exterior domains ⋮ The Fujita exponent for semilinear heat equations with quadratically decaying potential or in an exterior domain ⋮ Nonexistence of solutions for the quasilinear parabolic differential inequalities with singular potential term and nonlocal source

Cites Work

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• Existence and nonexistence of global solutions for \(u_ t = \Delta u + a(x)u^ p\) in \(\mathbb{R}^ d\)
• Large time behaviors of hot spots for the heat equation with a potential
• Asymptotic behavior of solutions for some semilinear heat equations in \(\mathbb R^N\)
• Existence and non-existence of global solutions for a semilinear heat equation
• On the growing problem for semilinear heat equations
• Multidimensional nonlinear diffusion arising in population genetics
• The role of critical exponents in blow-up theorems: The sequel
• The Role of Critical Exponents in Blowup Theorems
• The quantizing effect of potentials on the critical number of reaction-diffusion equations

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