Accession Number : AD0663075

Title :   AN A PRIORI ESTIMATE FOR SOME QUASI-LINEAR PARABOLIC SYSTEMS. I.,

Corporate Author : JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB

Personal Author(s) : Venttsel,T. D.

Report Date : 23 OCT 1967

Pagination or Media Count : 8

Abstract : Considered is the boundary-value problem for systems of the form A (the second partial derivative of u with respect to x) = (the partial derivative of u with respect to t) + the partial with respect to x of the quantity (grad phi (u)), u = (u sub 1 ..., u sub n), where A is a constant, positive-definite, symmetric matrix. The function phi (u) is assumed to have an exponential order of increase: phi (u) = O (the absolute value of u) superscript (p + 2). An a priori estimate for max (absolute value of u) is established for p < 3/2. The estimate is derived by comparing energy estimates obtainable for solutions of the problem being considered. It follows from the derived solution that a solution to the problem exists in the large.

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, *BOUNDARY VALUE PROBLEMS), BOUNDARY VALUE PROBLEMS, MATRICES(MATHEMATICS), INTEGRAL EQUATIONS, INEQUALITIES, APPROXIMATION(MATHEMATICS), USSR

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE