
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 initialboundary 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