Implicit Degenerate Evolution Equations and Applications.

Abstract

The initial-value problem is studied for evolution equations in Hilbert space of the general form d/dt A(u) + B(u) 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.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1980
Accession Number
ADA089637

Entities

People

  • Emmanuele Dibenedetto
  • R. E. Showalter

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Banach Space
  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Differential Equations
  • Diffusion
  • Energy
  • Equations
  • Formulas (Mathematics)
  • Heat Of Fusion
  • Hilbert Space
  • Identities
  • Mathematics
  • Partial Differential Equations
  • Personal Information Managers
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra

Technology Areas

  • Space