# Accession Number:

## ADA089637

# Title:

## Implicit Degenerate Evolution Equations and Applications.

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1980-07-01

# Pagination or Media Count:

## 41.0

# Abstract:

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.

# Descriptors:

# Subject Categories:

- Theoretical Mathematics