Approximation And Numerical Analysis Of Nonlinear Equations Of Evolution
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Approximation and Numerical Analysis of Nonlinear Equations of Evolution
Author | : J. T. Oden |
Publisher | : |
Total Pages | : 146 |
Release | : 1980 |
Genre | : |
ISBN | : |
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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).
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