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Very singular solutions to a nonlinear parabolic equation with absorption. I. Existence

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Publication:2710418
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DOI10.1017/S0308210500000779zbMath0973.35100MaRDI QIDQ2710418

Philippe Laurençot, Saïd Benachour

Publication date: 27 November 2001

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)


zbMATH Keywords

viscous Hamilton-Jacobi equation\(L^\infty\)-estimate for the fundamental solutions


Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55)


Related Items

Global solutions of the fast diffusion equation with gradient absorption terms ⋮ Complete classification of shape functions of self-similar solutions ⋮ The Cauchy problem for \(u_{t}=\Delta u+| \nabla u|^q\) ⋮ \(L^\infty \) estimates and uniqueness results for nonlinear parabolic equations with gradient absorption terms ⋮ The local theory for viscous Hamilton--Jacobi equations in Lebesgue spaces. ⋮ Asymptotic behavior for a singular diffusion equation with gradient absorption ⋮ Asymptotic profiles of solutions to convection-diffusion equations. ⋮ Self-similar singular solution of fast diffusion equation with gradient absorption terms ⋮ Asymptotic profiles of solutions to viscous Hamilton--Jacobi equations ⋮ The Cauchy problem for \(u_t=\Delta u+ |\nabla u|^q\), large-time behaviour



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