Singular Elliptic Problems: Bifurcation & Asymptotic Analysis

Name: Singular Elliptic Problems: Bifurcation & Asymptotic Analysis
Brand: Oxford University Press, USA
SKU: 9780195334722
Price: 12936.0 INR
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by Marius Ghergu , Vicentiu Radulescu

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ISBN13: 9780195334722
Binding: Hardcover
Subject: N/A
Publisher: Oxford University Press, USA
Publisher Imprint: Oxford University Press, USA
Publication Date: March 25, 2008
Pages: 298
Original Price: USD 120.0
Language: English
Edition: N/A
Item Weight: 590 grams
BISAC Subject(s): Differential Equations / Partial

About The Book

This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by singular elliptic equations. There are carefully analyzed logistic type equations with boundary blow-up solutions and generalized Lane-Emden-Fowler equations or Gierer-Meinhardt systems with singular nonlinearity in anisotropic media. These nonlinear problems appear as mathematical models in various branches of Physics, Mechanics, Genetics, Economics, Engineering, and they are also relevant in Quantum Physics and Differential Geometry.

One of the main purposes of this volume is to deduce decay rates for general classes of solutions in terms of estimates of particular problems. Much of the material included in this volume is devoted to the asymptotic analysis of solutions and to the qualitative study of related bifurcation problems. Numerical approximations illustrate many abstract results of this volume. A systematic description of the most relevant singular phenomena described in these lecture notes includes existence (or nonexistence) of solutions, unicity or multiplicity properties, bifurcation and asymptotic analysis, and optimal regularity.

The method of presentation should appeal to readers with different backgrounds in functional analysis and nonlinear partial differential equations. All chapters include detailed heuristic arguments providing thorough motivation of the study developed later on in the text, in relationship with concrete processes arising in applied sciences. The book includes an extensive bibliography and a rich index, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of nonlinear singular phenomena

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