Accession Number : ADA189383
Title : Numerical Solution of Ill Posed Problems in Partial Differential Equations.
Descriptive Note : Final technical rept. 1 Oct 84-30 Sep 87,
Corporate Author : IOWA STATE UNIV AMES DEPT OF MATHEMATICS
Personal Author(s) : Levine, Howard A
PDF Url : ADA189383
Report Date : Sep 1987
Pagination or Media Count : 27
Abstract : This project is concerned with several questions concerning the existence, uniqueness continuous data dependence and numerical computation of solutions of various ill posed problems in partial differential equations. Several problems involving reaction diffusion equations with and without convection terms present were studied. In the latter case the ability of finite element approximate solutions to reproduce the continuous time dynamics was investigated. In the former case a convective diffusion equation with a similar source in the boundary condition was analyzed. A fairly complete picture of the dynamics was obtained. With the source term in the equation, computations revealed a rich structure which has been partially analyzed theoretically. Several problems for reaction diffusion equations in unbounded regimes were also investigated. It was shown that under certain conditions in the rate law all nonzero solutions blow up in finite time, while for other conditions in the rate law, solutions damp out.
Descriptors : *NUMERICAL METHODS AND PROCEDURES, *PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARIES, COMPUTATIONS, CONVECTION, DIFFUSION, DYNAMICS, FINITE ELEMENT ANALYSIS, NUMERICAL ANALYSIS, RATES, SOLUTIONS(GENERAL), POTENTIAL THEORY, EIGENVALUES, CAUCHY PROBLEM
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE