Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations

AvVictor A. Galaktionov,Enzo L. Mitidieri

Inbunden, Engelska, 2014

Del i serien Chapman & Hall/CRC Monographs and Research Notes in Mathematics

2 306 kr

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Beskrivning

Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.The book first studies the particular self-similar singularity solutions (patterns) of the equations. This approach allows four different classes of nonlinear PDEs to be treated simultaneously to establish their striking common features. The book describes many properties of the equations and examines traditional questions of existence/nonexistence, uniqueness/nonuniqueness, global asymptotics, regularizations, shock-wave theory, and various blow-up singularities.Preparing readers for more advanced mathematical PDE analysis, the book demonstrates that quasilinear degenerate higher-order PDEs, even exotic and awkward ones, are not as daunting as they first appear. It also illustrates the deep features shared by several types of nonlinear PDEs and encourages readers to develop further this unifying PDE approach from other viewpoints.

Produktinformation

Utgivningsdatum:2014-09-22
Mått:156 x 234 x 35 mm
Vikt:964 g
Format:Inbunden
Språk:Engelska
Serie:Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Antal sidor:569
Förlag:Taylor & Francis Inc
ISBN:9781482251722

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Victor A. Galaktionov, Enzo L. Mitidieri, Stanislav I. Pohozaev

Recensioner i media

"This volume gives a collection of results on self-similar singular solutions for nonlinear partial differential equations (PDEs), with special emphasis on ‘exotic’ equations of higher order …"—Zentralblatt MATH 1320

Innehållsförteckning

Introduction. Complicated Self-Similar Blow-Up, Compacton, and Standing Wave Patterns for Four Nonlinear PDEs: A Unified Variational Approach to Elliptic Equations. Classification of Global Sign-Changing Solutions of Semilinear Heat Equations in the Subcritical Fujita Range: Second- and Higher-Order Diffusion. Global and Blow-Up Solutions for Kuramoto–Sivashinsky, Navier–Stokes, and Burnett Equations. Regional, Single-Point, and Global Blow-Up for a Fourth-Order Porous Medium-Type Equation with Source. Semilinear Fourth-Order Hyperbolic Equation: Two Types of Blow-Up Patterns. Quasilinear Fourth-Order Hyperbolic Boussinesq Equation: Shock, Rarefaction, and Fundamental Solutions. Blow-Up and Global Solutions for Korteweg–de Vries-Type Equations. Higher-Order Nonlinear Dispersion PDEs: Shock, Rarefaction, and Blow-Up Waves. Higher-Order Schrödinger Equations: From "Blow-Up" Zero Structures to Quasilinear Operators. References.