A singular solution with smooth initial data for a semilinear parabolic equation

DOI10.1016/j.na.2010.10.010zbMath1208.35081OpenAlexW2085912210MaRDI QIDQ622410

Shota Sato

Publication date: 31 January 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.10.010

zbMATH Keywords

power nonlinearityHaraux-Weissler equation

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Initial value problems for second-order parabolic equations (35K15) Semilinear parabolic equations (35K58) Self-similar solutions to PDEs (35C06)

Related Items (3)

Convergence rate to singular steady states in a semilinear parabolic equation ⋮ Unnamed Item ⋮ Positive solutions with a time-independent boundary singularity of semilinear heat equations in bounded Lipschitz domains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Remarks on the large time behaviour of a nonlinear diffusion equation
• Radial symmetry of self-similar solutions for semilinear heat equations
• Existence of positive weak solutions with a prescribed singular set of semilinear elliptic equations
• Regular self-similar solutions of the nonlinear heat equation with initial data above the singular steady state
• Asymptotic behavior of solutions of a semilinear heat equation with subcritical nonlinearity
• Solutions with moving singularities for a semilinear parabolic equation
• Quasilinear Dirichlet problems driven by positive sources
• Forward self-similar solution with a moving singularity for a semilinear parabolic equation
• An ODE approach to the multiplicity of self-similar solutions for semi-linear heat equations

This page was built for publication: A singular solution with smooth initial data for a semilinear parabolic equation