Global existence and decreasing property of boundary values of solutions to parabolic equations with nonlocal boundary conditions

Sangwon Seo

Vol. 193 (2000), No. 1, 219–226

DOI: 10.2140/pjm.2000.193.219

Abstract

It is shown that the local solution of parabolic equation with nonlocal boundary condition representing entropy can be extended to whole time domain for weights with large L¹ norms. When the weight is identically zero on some part of the boundary, it is shown that the boundary values can decrease even when the other weights are some large.

Milestones

Received: 29 July 1998

Revised: 3 September 1998

Published: 1 March 2000