Symmetry and Separation of Variables
by Willard Miller
Publisher: Addison-Wesley 1977
Number of pages: 318
Originally published in 1977, this volume is concerned with the relationship between symmetries of a linear second-order partial differential equation of mathematical physics, the coordinate systems in which the equation admits solutions via separation of variables, and the properties of the special functions that arise in this manner.
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by Marco Squassina - Electronic Journal of Differential Equations
A survey of results about existence, multiplicity, perturbation from symmetry and concentration phenomena for a class of quasi-linear elliptic equations coming from functionals of the calculus of variations which turn out to be merely continuous.
by G.B. Folland - Tata Institute of Fundamental Research
The purpose of this course was to introduce students to the applications of Fourier analysis -- by which I mean the study of convolution operators as well as the Fourier transform itself -- to partial differential equations.
by K. Yosida - Tata Institute of Fundamental Research
In these lectures, we shall be concerned with the differentiability and the representation of one-parameter semi-groups of bounded linear operators on a Banach space and their applications to the initial value problem for differential equations.
by Valeriy Serov - University of Oulu
Contents: Preliminaries; Local Existence Theory; Fourier Series; One-dimensional Heat Equation; One-dimensional Wave Equation; Laplace Equation; Laplace Operator; Dirichlet and Neumann Problems; Layer Potentials; The Heat Operator; The Wave Operator.