Accession Number : AD0650398

Title :   ON SOME PROPERTIES OF GENERALIZED SOLUTIONS OF LINEAR EQUATIONS OF ELLIPTIC AND PARABOLIC TYPE.

Descriptive Note : APL library bulletin translation series,

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

Personal Author(s) : Ivanov,A. V.

Report Date : 08 MAR 1967

Pagination or Media Count : 16

Abstract : Considered are weak solutions in W(1,0)sub 2 (Omega x (0,T)) (omega is a space domain) of linear parabolic equation delta u/delta t - Lu = f + div g, where L is the sum of an elliptic second-order operator in divergence form plus lower-order terms. The existence and uniqueness theory of Ladyzhenskaya and Ural'tseva for weak solutions of the first mixed problem involves requiring that the lower-order terms be in certain L sub p classes. It is shown by example that some of these requirements are necessary for uniqueness. Some similar results are also given concerning elliptic problems and concerning the Holder continuity of the solutions. (Author)

Descriptors :   (*EQUATIONS, *PARTIAL DIFFERENTIAL EQUATIONS), OPERATORS(MATHEMATICS), BOUNDARY VALUE PROBLEMS, USSR

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE