โ Scribed by Viorel Barbu (auth.)
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The material of the present book has been used for graduate-level courses at the University of Ia~i during the past ten years. It is a revised version of a book which appeared in Romanian in 1993 with the Publishing House of the Romanian Academy. The book focuses on classical boundary value problems for the principal equations of mathematical physics: second order elliptic equations (the Poisson equations), heat equations and wave equations. The existence theory of second order elliptic boundary value problems was a great challenge for nineteenth century mathematics and its development was marked by two decisive steps. Undoubtedly, the first one was the Fredholm proof in 1900 of the existence of solutions to Dirichlet and Neumann problems, which represented a triumph of the classical theory of partial differential equations. The second step is due to S. 1. Sobolev (1937) who introduced the concept of weak solution in partial differential equations and inaugurated the modern theory of boundary value problems. The classical theory which is a product ofthe nineteenth century, is concerned with smooth (continuously differentiable) sollutions and its methods rely on classical analysis and in particular on potential theory. The modern theory concerns distributional (weak) solutions and relies on analysis of Sob ole v spaces and functional methods. The same distinction is valid for the boundary value problems associated with heat and wave equations. Both aspects of the theory are present in this book though it is not exhaustive in any sense.
Front Matter....Pages N1-xii
Preliminaries....Pages 1-22
Elliptic Boundary Value Problems....Pages 23-92
Elliptic Problems in Sobolev Spaces....Pages 93-180
The Heat Equation....Pages 181-236
The Wave Equation....Pages 237-275
Back Matter....Pages 276-284
Partial Differential Equations; Applications of Mathematics; Potential Theory; Calculus of Variations and Optimal Control; Optimization
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Book was ordered on June 1st 2009. As of today July 7th, 2009 10:35pm, item has not arrived. I have placed a claim with amazon.com. It seems that seller does not keep up with sales.
Boundary Value Problems, Sixth Edition, is the leading text on boundary value problems and Fourier series for professionals and students in engineering, science, and mathematics who work with partial differential equations. In this updated edition, author David Powers provides a thorough overview of
This example-rich reference fosters a smooth transition from elementary ordinary differential equations to more advanced concepts. Asmar's relaxed style and emphasis on applications make the material accessible even to readers with limited exposure to topics beyond calculus.Encourages computer for i
Boundary Value Problems is the leading text on boundary value problems and Fourier series for professionals and students in engineering, science, and mathematics who work with partial differential equations.In this updated edition, author David Powers provides a thorough overview of solving boundary