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

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

Inbunden, Engelska, 2014

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

3 019 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

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

Utgivningsdatum2014-09-22
Mått156 x 234 x 35 mm
Vikt964 g
FormatInbunden
SpråkEngelska
SerieChapman & Hall/CRC Monographs and Research Notes in Mathematics
Antal sidor569
FörlagTaylor & Francis Inc
ISBN9781482251722

Tillhör följande kategorier

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.