Accession Number : ADA116178

Title :   Quasinonlinear Evolution Equations.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Crandall,Michael G. ; Souganidis,Panagiotis E.

Report Date : MAR 1982

Pagination or Media Count : 45

Abstract : A very substantial theory of quasilinear evolution equations, which applies to many problems of mathematical physics, has been developed by T. Kato. The theory obtains solutions of quasilinear problems via contraction mappings which are defined by means of a theory of linear evolution equations also developed by Kato. In the current work we show how existence theorems, etc. may be proved in the simplest of the settings considered by Kato via discretization in time. This method does not require an intervening linear theory and also may be viewed as giving results - admittedly crude - about numerical approximation of some of Kato's examples. Since the hypothesis of quasilinearity is not used explicitly herein, we employ the term quasinonlinear for the equations dealt with. (Author)

Descriptors :   *Nonlinear algebraic equations, *Evolution(General), Approximation(Mathematics), Hypotheses, Physics, Theory, Numerical analysis, Mapping, Methodology

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE