Partial Differential Equations with Multiple Characteristics
Published on 20. October 1997
Book
Hardback
352 pages
978-3-05-501764-3 (ISBN)
Description
This text concentrates on the general theory of partial differential equations with multiple characteristics. The methods of microlocal analysis are reviewed and used to support results on local solvability, hypoellipticity, propagation of singularities in the frame of Sobolev spaces, Schwartz distributions and Gevrey ultradistributions. The Cauchy problem is also considered.
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Content
An introduction to linear PDE - generalized functions and wave front sets, pseudodifferential operators and Fourier integral operators; linear PDE with multiple characteristics - the symplectic case, the involutive case, perturbations of powers of operators of principal type; general theory for nonlinear PDE - local solvability for nonlinear equations with multiple characteristics.