On blow-up sets and asymptotic behavior of interfaces of one dimensional quasilinear degenerate parabolic equations

DOI10.2977/prims/1195169661zbMath0789.35024OpenAlexW1997412303MaRDI QIDQ1190731

Ryuichi Suzuki

Publication date: 26 September 1992

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195169661

zbMATH Keywords

Cauchy problemDirichlet conditionsinitial boundary value problemblow-up setNeumann conditionsquasilinear degenerate parabolic equationbehavior of the interface near the blow-up timeshape of the blow-up set

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Degenerate parabolic equations (35K65) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (4)

ON THE QUALITATIVE BEHAVIOR OF SOLUTIONS TO CERTAIN REACTION DIFFUSION EQUATION IN LARGE DOMAIN ⋮ Nonexistence of solutions for a degenerate parabolic equation describing imperfect ignition ⋮ Positivity preserving high-order local discontinuous Galerkin method for parabolic equations with blow-up solutions ⋮ Total blow-up of a quasilinear heat equation with slow-diffusion for non-decaying initial data

Cites Work

• Convergence, asymptotic periodicity, and finite-point blow-up in one- dimensional semilinear heat equations
• A note on the blowup-nonblowup problems in nonlinear parabolic equations
• On blow-up of solutions for quasilinear degenerate parabolic equations
• Stabilization of solutions of a degenerate nonlinear diffusion problem
• Positivity versus localization in degenerate diffusion equations
• The zero set of a solution of a parabolic equation.
• The Porous Medium Equation in One Dimension
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