Singular Elliptic Problems
Bifurcation and Asymptotic Analysis
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Singular Elliptic Problems by Marius Ghergu
Book DescriptionThis 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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Book DetailsISBN: 9780195334722
(240mm x 160mm x 20mm)
Imprint: Oxford University Press Inc
Publisher: Oxford University Press Inc
Publish Date: 24-Apr-2008
Country of Publication: United States
Books By Author Marius Ghergu
Isolated Singularities in Partial Differential Inequalities, Hardback (January 2016)» View all books by Marius Ghergu
Presents powerful methods for dealing with singularities in elliptic and parabolic partial differential inequalities.
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Author Biography - Marius Ghergu
Marius Ghergu is Researcher at the Institute of Mathematics "Simion Stoilow" of the Romanian Academy. Vicentiu Radulescu is Senior Researcher at the Institute of Mathematics "Simion Stoilow" of the Romanian Academy and Full Professor at the University of Craiova.
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