Why the Boundary of a Round Drop Becomes a Curve of Order Four
by A. N. Varchenko, P. I. Etingof
Publisher: American Mathematical Society 1992
Number of pages: 72
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. This text discusses this topic and other recent work in the theory of fluid flows with a moving boundary.
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by Boris Dubrovin - SISSA
These are lecture notes on various topics in analytic theory of differential equations: Singular points of solutions to analytic differential equations; Monodromy of linear differential operators with rational coefficients.
by A. Volpert, V. Volpert, V. Volpert - American Mathematical Society
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 and their stability.
by Paul Dawkins - Lamar University
Contents: Basic Concepts; First Order Differential Equations; Second Order DE; Laplace Transforms; Systems of Differential Equations; Series Solutions; Higher Order DE; Boundary Value Problems and Fourier Series; Partial Differential Equations.
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These are lecture notes from Real analysis and PDE: Basic Topological, Metric and Banach Space Notions; Riemann Integral and ODE; Lebesbgue Integration; Hilbert Spaces and Spectral Theory of Compact Operators; Complex Variable Theory; etc.