Collapse of the solutions of parabolic and hyperbolic equations with nonlinear boundary conditions

DOI10.1007/BF01103721zbMath0544.35060OpenAlexW2089368442MaRDI QIDQ796748

Varga K. Kalantarov

Publication date: 1984

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01103721

zbMATH Keywords

nonlinear boundary conditionscollapse of solutionsmethod of concavity

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Shocks and singularities for hyperbolic equations (35L67) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60)

Related Items (5)

A potential well theory for the heat equation with a nonlinear boundary condition ⋮ The blow-up rate for a coupled system of semilinear heat equations with nonlinear boundary conditions ⋮ The blow-up rate for a strongly coupled system of semilinear heat equations with nonlinear boundary conditions ⋮ Blow up for some quasilinear equations with dynamical boundary conditions of parabolic type ⋮ Non-existence results for a semilinear hyperbolic problem with boundary condition of memory type

Cites Work

• The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types
• Blow-up of solutions of nonlinear wave equations in three space dimensions
• Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time
• Some Nonexistence Theorem for Initial-Boundary Value Problems with Nonlinear Boundary Constraints

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