AN A PRIORI ESTIMATE FOR SOME QUASI-LINEAR PARABOLIC SYSTEMS. I.,
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 23, 1967
- Accession Number
- AD0663075
Entities
People
- T. D. Venttsel
Organizations
- Johns Hopkins University Applied Physics Laboratory