Blow-up in Quasilinear Parabolic Equations

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The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics.

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Editorial Board

Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil
Walter D. Neumann, Columbia University, New York, USA
Markus J. Pflaum, University of Colorado, Boulder, USA
Dierk Schleicher, Jacobs University, Bremen, Germany
Katrin Wendland, University of Freiburg, Germany

Honorary Editor

Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia

Titles in planning include

Yuri A. Bahturin, Identical Relations in Lie Algebras (2019)
Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019)
Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019)
Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021)
Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

 

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Contents

Chapter
1
Generalized solutions of quasilinear degenerate parabolic equations
14
Remarks and comments on the literature
35
Asymptotic stability of the fundamental solution of the Cauchy problem
47
Asymptotic stability of selfsimilar solutions of nonlinear heat equations
53
Quasilinear heat equation in a bounded domain
61
The fast diffusion equation Boundary value problems in a bounded
67
Conditions of equivalence of different quasilinear heat equations
74
Proof of localization of unbounded solutions for B 2 0 + 1 absence
238
Asymptotic stability of unbounded selfsimilar solutions
257
Blowup regimes effective localization for semilinear equations with
274
Remarks and comments on the literature
306
The operator functional comparison method for solutions of parabolic
324
Conditions for absence of heat localization
348
Criticality conditions and a comparison theorem for finite difference
365
Chapter VI
373

A heat equation with a gradient nonlinearity
84
Selfsimilar solutions of the semilinear parabolic equation
93
A nonlinear heat equation with a source and a sink
99
The structure of attractor of the semilinear parabolic equation with
107
Remarks and comments on the literature
124
Heat localization inertia
130
Effective heat localization
158
Remarks and comments on the literature
174
Asymptotic behaviour of unbounded solutions Qualitative theory
200
Conditions for finite time blowup Globally existing solutions
214
Approximate selfsimilar solutions in the nondegenerate case
386
Approximate selfsimilar solutions in the nondegenerate case Integral
398
Remarks and comments on the literature
413
Boundary value problems in bounded domains
430
A parabolic system of quasilinear equations with a source
447
The combustion localization phenomenon in multicomponent media
467
Finite difference schemes for quasilinear parabolic equations admitting
476
Remarks and comments on the literature
502
Index 535
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Page 515 - Asymptotic stability and blowing up of solutions of some nonlinear equations, J. Differential Equations, 26 (1977), 291-319.
Page 521 - Finite element analysis of the semi-linear heat equation of blow-up type. Topics in numerical analysis III.

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