A class of semilinear parabolic equations with singular initial data

DOI10.1016/J.NA.2008.03.025zbMath1169.35343OpenAlexW2014784965MaRDI QIDQ1004645

Daisuke Hirata

Publication date: 11 March 2009

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.2008.03.025

zbMATH Keywords

existenceinitial-boundary value problemsemilinear parabolic equationcritical Sobolev spacesubquadratic casequadratic casesingular Sobolev class

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Initial-boundary value problems for second-order parabolic equations (35K20) Critical exponents in context of PDEs (35B33)

Cites Work

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• Existence and non-existence of global solutions for a semilinear heat equation
• The Cauchy problem for \(u_{t}=\Delta u+| \nabla u|^q\)
• The local theory for viscous Hamilton--Jacobi equations in Lebesgue spaces.
• Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions
• A nonlinear heat equation with singular initial data
• Admissible L_p norms for local existence and for continuation in semilinear parabolic systems are not the same
• Global existence and decay for viscous Hamilton-Jacobi equations

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