Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics
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A01=Sergey R. Svirshchevskii
A01=Victor A. Galaktionov
advanced nonlinear PDE solution techniques
Author_Sergey R. Svirshchevskii
Author_Victor A. Galaktionov
Category=PBKJ
Category=PBWH
Category=PBWR
compacton solutions
discrete operator methods
eq_isMigrated=1
eq_nobargain
gas dynamics theory
nonlinear evolution equations
reaction diffusion models
thin film analysis
Product details
- ISBN 9780367389970
- Weight: 453g
- Dimensions: 156 x 234mm
- Publication Date: 19 Sep 2019
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Paperback
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Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties.
This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders.
The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.
Galaktionov, Victor A.; Svirshchevskii, Sergey R.
