Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications

Victor A. Galaktionov (University of Bath, UK), Goong Chen, Thomas J. Bridges (University of Surrey, UK)

$305

Hardback

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English

Chapman & Hall/CRC
24 May 2004

Differential calculus & equations

Series: Chapman & Hall/CRC Applied Mathematics & Nonlinear Science

Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century. Briefly revived by Polya in the 1930's and rediscovered in part several times since, it was not

until the 1980's that the Sturmian argument for PDEs began to penetrate into the theory of parabolic equations and was found to have several fundamental applications.

Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications focuses on geometric aspects of the intersection comparison for nonlinear models creating finite-time singularities. After introducing the original Sturm zero set results for linear parabolic equations and the basic concepts of geometric

analysis, the author presents the main concepts and regularity results of the geometric intersection theory (G-theory).

Here he considers the general singular equation and presents the geometric notions related to the regularity and interface propagation of solutions. In the general setting, the author describes the main aspects of the ODE-PDE duality, proves existence and nonexistence theorems, establishes uniqueness and optimal Bernstein-type estimates, and derives interface equations, including higher-order equations. The final two chapters explore some special aspects of discontinuous and continuous limit

semigroups generated by singular parabolic equations.

Much of the information presented here has never before been published in book form. Readable and self-contained, this book forms a unique and outstanding reference on second-order parabolic PDEs used as models for a wide range of physical problems.

By: Victor A. Galaktionov (University of Bath UK)
Series edited by: Goong Chen, Thomas J. Bridges (University of Surrey, UK)
Imprint: Chapman & Hall/CRC
Country of Publication: United States
Dimensions: Height: 234mm, Width: 156mm, Spine: 25mm
Weight: 671g
ISBN: 9781584884620
ISBN 10: 1584884622
Series: Chapman & Hall/CRC Applied Mathematics & Nonlinear Science
Pages: 384
Publication Date: 24 May 2004
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Victor A. Galaktionov

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Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications

Victor A. Galaktionov (University of Bath, UK), Goong Chen, Thomas J. Bridges (University of Surrey, UK)

$305

Hardback

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