Partial Differential Equations (Lectures in Applied Mathematics, Vol. 3)

Science & Math

Martin Schechter

Fritz John

Lipman Bers

Mathematics

John Wiley&Sons, Inc.

<p>This collection of results on partial differential equations employs certain elementary identities for plane and spherical integrals of an arbitrary function, showing how a variety of results on fairly general differential equations follow from those identities. Explores the decomposition of arbitrary functions into functions of the type of plane waves; Radon transformation; more. 1955 edition.</p>

Plane Waves and Spherical Means: Applied to Partial Differential Equations (Dover Books on Mathematics)

Dover `

Lectures on Advanced Numerical Analysis

Gordon & Breach

This is the second volume in the University Lecture Series, designed to make more widely available some of the outstanding lectures presented in various institutions around the country. Each year at Lehigh University, a distinguished mathematical scientist presents the Pitcher Lectures in the Mathematical Sciences. This volume contains the Pitcher lectures presented by Fritz John in April 1989. The lectures deal with existence in the large of solutions of initial value problems for nonlinear hyperbolic partial differential equations. As is typical with nonlinear problems, there are many results and few general conclusions in this extensive subject, so the author restricts himself to a small portion of the field, in which it is possible to discern some general patterns. Presenting an exposition of recent research in this area, the author examines the way in which solutions can, even with small and very smooth initial data, ``blow up'' after a finite time. For various types of quasi-linear equations, this time depends strongly on the number of dimensions and the ``size'' of the data. Of particular interest is the formation of singularities for nonlinear wave equations in three space dimensions.

Nonlinear Wave Equations, Formation of Singularities (University Lecture Series)

American Mathematical Society

Partial Differential Equations (Applied Mathematical Sciences Vol. 1)

Reference

Foreign Language Study & Reference

Springer, Verlag

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