Accession Number : AD0755073

Title :   A Nonexistence Theorem for the Heat Equation with a Nonlinear Boundary Condition and for the Porous Medium Equation Backward in Time.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Levine,Howard A. ; Payne,Lawrence E.

Report Date : DEC 1972

Pagination or Media Count : 23

Abstract : The paper deals with two nonlinear problems for parabolic equations. The first, problem A, is an initial-boundary value problem for the heat equation where the nonlinearity is in the boundary condition. The second, problem B, is a final value problem for the porous medium equation. It is shown that if the nonlinearity and initial data in A satisfy certain restrictions then no classical (or weak) solution of A can exist for all time. It is further shown that no weak solution of B can have existed for all previous time. An indication is given of how the methods used in A can be used to obtain (under reasonable hypotheses) the same type of nonexistence result for nonlinear problems associated with certain systems of parabolic and hyperbolic equations. (Author)

Descriptors :   (*HEAT TRANSFER, *PARTIAL DIFFERENTIAL EQUATIONS), BOUNDARY VALUE PROBLEMS, BOUNDARY VALUE PROBLEMS, NONLINEAR DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION, THEOREMS

Subject Categories : Numerical Mathematics
      Thermodynamics

Distribution Statement : APPROVED FOR PUBLIC RELEASE