Der Text behandelt neue Methoden zur Lösung nichtlinearer parabolischer Evolutionsgleichungen und faßt die Untersuchungen führender russischer Mathematiker innerhalb der letzten zwanzig Jahre erstmals in Buchform zusammen.
Der Text behandelt neue Methoden zur Lösung nichtlinearer parabolischer Evolutionsgleichungen und faßt die Untersuchungen führender russischer Mathematiker innerhalb der letzten zwanzig Jahre erstmals in Buchform zusammen.
Summery of contents: 1. Preliminary facts of the theory of second order quasilinear parabolic equations 2. Some quasilinear parabolic equations. Self-similar solutions and their asymptotic stability 3. Heat localization (inertia) 4. Nonlinear equation with a source. Blow-up regimes. Localization. Asymptotic behaviour of solutions. 5. Methods of generalized comparison of solutions of different nonlinear parabolic equations and their application. 6. Approximate self-similar solutions of nonlinear heat equations and their applications in the study of the localization effect 7. Some other methods of study of unbounded solutions
Summery of contents: 1. Preliminary facts of the theory of second order quasilinear parabolic equations 2. Some quasilinear parabolic equations. Self-similar solutions and their asymptotic stability 3. Heat localization (inertia) 4. Nonlinear equation with a source. Blow-up regimes. Localization. Asymptotic behaviour of solutions. 5. Methods of generalized comparison of solutions of different nonlinear parabolic equations and their application. 6. Approximate self-similar solutions of nonlinear heat equations and their applications in the study of the localization effect 7. Some other methods of study of unbounded solutions
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