SINGULAR SOLUTIONS TO THE HEAT EQUATIONS WITH NONLINEAR ABSORPTION AND HARDY POTENTIALS

DOI10.1142/S0219199712500137zbMath1298.35100arXiv1009.4591MaRDI QIDQ5388171

Vitali Liskevich, Zeev Sobol, Andrey E. Shishkov

Publication date: 18 April 2012

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.4591

zbMATH Keywords

semilinear heat equationHardy potentialsource-type solutionvery singular solution

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Initial value problems for second-order parabolic equations (35K15) Semilinear parabolic equations (35K58) Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian (35K91)

Related Items

An approach without using Hardy inequality for the linear heat equation with singular potential ⋮ Qualitative analysis of solutions to a nonlocal Choquard–Kirchhoff diffusion equations in ℝN$$ {\mathbb{R}}^N $$ ⋮ On the heat equation with nonlinearity and singular anisotropic potential on the boundary ⋮ On the evolution equation with a dynamic Hardy-type potential ⋮ Initial-boundary value problem for a fourth-order plate equation with Hardy-Hénon potential and polynomial nonlinearity

Cites Work

• Unnamed Item
• Unnamed Item
• Classification of singular solutions of a nonlinear heat equation
• Singular solutions of some nonlinear parabolic equations with spatially inhomogeneous absorption
• Conservativeness and extensions of Feller semigroups
• Singular solutions of some nonlinear parabolic equations
• Heat kernel bounds and desingularizing weights.
• Stability results for Harnack inequalities.
• On the \(L_{p}\)-theory of \(C_{0}\)-semigroups associated with second-order elliptic operators. II
• Estimates of integral kernels for semigroups associated with second-order elliptic operators with singular coefficients
• Positive super-solutions to semi-linear second-order non-divergence type elliptic equations in exterior domains
• Influence of the Hardy potential in a semilinear heat equation
• Variational problems related to self-similar solutions of the heat equation

This page was built for publication: SINGULAR SOLUTIONS TO THE HEAT EQUATIONS WITH NONLINEAR ABSORPTION AND HARDY POTENTIALS