Approximation and Numerical Analysis of Nonlinear Equations of Evolution.
Abstract
Important results were obtained in four areas: (1) Existence theorems, approximation theorems, a priori error estimates, numerical schemes, and finally computer codes were developed for the analysis of one-and two-dimensional, one- and two-phase Stefan problems characterized by variational inequalities; (2) Existence theorems, uniqueness theorems, theorems on the stability and asymptotic stability of solutions, and regularity of solutions were developed for a large class of nonlinear, convective diffusion problems characterized by pseudo-monotone operators; (3) A priori error estimates for Galerkin and Faedo-Galerkin approximations (defined, in general, by finite element methods) were established for nonlinear convection diffusion problems involving general pseudomonotone operators; and (4) Existence theorems were obtained for a large class of nonlinear, degenerate evolution equations with solutions involving free boundaries. Applications to porous media and two-phase Stephan problems were completed. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 31, 1980
- Accession Number
- ADA082452
Entities
People
- J. T. Oden
Organizations
- University of Texas at Austin