No LocalL1Solution for a Nonlinear Heat Equation

DOI10.1081/PDE-120025486zbMath1053.35069MaRDI QIDQ4446119

Zhengfang Zhou, Canan Çelik

Publication date: 25 January 2004

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

zbMATH Keywords

mixed boundary conditionDirichlet boundary valuecutoff function argument

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) 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 (12)

Local existence for evolution equations with nonlocal term in time and singular initial data ⋮ A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces ⋮ Well-posedness of semilinear heat equations in \(L^1\) ⋮ Non-existence of local solutions of semilinear heat equations of Osgood type in bounded domains ⋮ Existence of solutions to fractional semilinear parabolic equations in Besov-Morrey spaces ⋮ Solvability for time‐fractional semilinear parabolic equations with singular initial data ⋮ Around a singular solution of a nonlocal nonlinear heat equation ⋮ Local existence and non-existence for a fractional reaction-diffusion equation in Lebesgue spaces ⋮ A doubly critical semilinear heat equation in the \(L^1\) space ⋮ On the local existence for a weakly parabolic system in Lebesgue spaces ⋮ Solvability of a Semilinear Parabolic Equation with Measures as Initial Data ⋮ On the local existence for Hardy parabolic equations with singular initial data

Cites Work

• Unnamed Item
• Unnamed Item
• Solutions for semilinear parabolic equations in \(L^ p\) and regularity of weak solutions of the Navier-Stokes system
• Semilinear evolution equations in Banach spaces
• Existence and non-existence of global solutions for a semilinear heat equation
• On the growing problem for semilinear heat equations
• A nonlinear heat equation with singular initial data
• Non-unicité des solutions d'une équation d'évolution non-linéaire
• On nonexistence of global solutions of some semilinear parabolic differential equations

This page was built for publication: No LocalL¹Solution for a Nonlinear Heat Equation