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:

1972-12-01

Pagination or Media Count:

23.0

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