Implicit Degenerate Evolution Equations and Applications.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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The initial-value problem is studied for evolution equations in Hilbert space of the general form ddt Au Bu not an element of f where A and B are maximal monotone operators. Existence of a solution is proved when A is a subgradient and either A is strongly-monotone or B is coercive existence is established also in the case where A is strongly-monotone and B is subgradient. Uniqueness is proved when one of A or B is continuous self-adjoint and the sum is strictly-monotone examples of nonuniqueness are given. Applications are indicated for various classes of degenerate nonlinear partial differential equations or systems of mixed elliptic-parabolic-pseudoparabolic types and problems with non-local nonlinearity.
- Theoretical Mathematics