Traveling Wave Solutions of Parabolic Systems
by A. Volpert, V. Volpert, V. Volpert
Publisher: American Mathematical Society 2000
Number of pages: 448
The theory of traveling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a general picture of current results about wave solutions of parabolic systems, their existence, stability, and bifurcations. The main part of the book contains original approaches developed by the authors.
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by Jeffrey R. Chasnov - The Hong Kong University of Science &Technology
Contents: A short mathematical review; Introduction to odes; First-order odes; Second-order odes, constant coefficients; The Laplace transform; Series solutions; Systems of equations; Bifurcation theory; Partial differential equations.
by Jiří Lebl - Lulu.com
One semester introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, and the Laplace transform.
by M. Kuranishi - Tata Institute of Fundamental Research
Contents: Parametrization of sets of integral submanifolds (Regular linear maps, Germs of submanifolds of a manifold); Exterior differential systems (Differential systems with independent variables); Prolongation of Exterior Differential Systems.
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This book concerns the problem of evolution of a round oil spot surrounded by water when oil is extracted from a well inside the spot. It turns out that the boundary of the spot remains an algebraic curve of degree four in the course of evolution.