Error Bounds and Uniqueness for the Solutions of Nonlinear, Strongly Coupled, Parabolic Systems of Differential Equations.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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The boundary value problem for a nonlinear, strongly coupled, parabolic system of differential equations in a box is considered. The system consists of 2 equations with 3 unknowns. The right sides of the differential equation satisfy Lipschitz conditions. Error bounds for an approximate solution are given. A uniqueness theorem is proven. The results are derived with the aid of the theory of differential inequalities and by using a theorem of Kolmogorov for the solution of the Landau problem.
- Theoretical Mathematics