| Description |
1 online resource (xxiv, 543 pages) : illustrations |
| Series |
Monographs and research notes in mathematics |
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Monographs and research notes in mathematics.
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| Contents |
1. Complicated self-similar blow-up, compacton, and standing wave patterns for four nonlinear PDEs: a unified variational approach to elliptic equations -- 2. Classification of global sign-changing solutions of semilinear heat equations in the subcritical Fujita range: second- and higher-order diffusion -- 3. Global and blow-up solutions for Kuramoto-Sivashinsky, Navier-Stokes, and Burnett equations -- 4. Regional, single-point, and global blow-up for a fourth- order porous medium-type equation with source -- 5. Semilinear fourth-order hyperbolic equation: two types of blow-up patterns -- 6. Quasilinear fourth-order hyperbolic Boussinesq equation : shock, rarefaction, and fundamental solutions -- 7. Blow-up and global solutions for Korteweg-de Vries-type equations -- 8. Higher-order nonlinear dispersion PDEs : shock, rarefaction, and blow-up waves -- 9. Higher-order Schrödinger equations : from"blow-up" zero structures to quasilinear operators |
| Summary |
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 ma |
| Bibliography |
Includes bibliographical references (pages 515-535) and index |
| Notes |
English |
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Print version record |
| Subject |
Blowing up (Algebraic geometry)
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Singularities (Mathematics)
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Differential equations, Parabolic.
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Differential equations, Hyperbolic.
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Schrödinger equation.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Blowing up (Algebraic geometry)
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Differential equations, Hyperbolic
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Differential equations, Parabolic
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Schrödinger equation
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Singularities (Mathematics)
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| Form |
Electronic book
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| Author |
Mitidieri, Enzo, author.
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Pokhozhaev, S. I., author.
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| ISBN |
9781482251739 |
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1482251736 |
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9781482251722 |
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1482251728 |
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0429160690 |
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9780429160691 |
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