Global Solutions of Semilinear Evolution Equations Satisfying an Energy Inequality.

Abstract

We prove the global existence (in time) for any solution of an abstract semilinear evolution equation in Hilbert space provided the solution satisfies an energy inequality and the nonlinearity does not exceed a certain growth rate. Ween applied to semilinear parabolic initial-boundary-value problems the result admits also the limiting growth rates which were given by Sobolevskii and Friedman, but which were not permitted in their theorem. The Navier-Stokes system in two dimensions is a special case of our general result. The method is based on the theories of semigroups and fractional powers of regularly accretive linear operators and on a nonlinear integral inequality which gives the crucial a-priori estimate for global existence. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1978
Accession Number
ADA063967

Entities

People

  • Hansjoerg Kielhoefer

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Banach Space
  • Boundary Value Problems
  • Contracts
  • Differential Equations
  • Equations
  • Hilbert Space
  • Inequalities
  • Integral Equations
  • Integrals
  • Mathematics
  • Navier Stokes Equations
  • New York
  • North Carolina
  • Partial Differential Equations
  • Sequences
  • Topology
  • United States

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space