POINTWISE BOUNDS FOR SOLUTIONS OF THE SECOND INITIAL-BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS.

Abstract

An extension is given of the method to obtain pointwise bounds for the solutions of the first initial-boundary value problem for a semilinear parabolic equation. A method is given for obtaining interior pointwise bounds for solutions of the second initial-boundary value problem. The bounds obtained are in terms of L(2) integrals of the initial-boundary data; thus close bounds may be obtained, in the linear case, by applying the Rayleigh-Ritz Technique. The approximating functions used in the procedure need not satisfy either the differential equation or the initial-boundary data but only certain regularity conditions. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1965
Accession Number
AD0630046

Entities

People

  • V. G. Sigillito

Organizations

  • Johns Hopkins University Applied Physics Laboratory

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Differential Equations
  • Equations
  • Integrals

Fields of Study

  • Mathematics

Readers

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