Continuous data dependence, regularization, and a three lines theorem for the heat equation with data in a space like direction
Tóm tắt
Let u(¦x¦, t) (for x∈RN, t>0) be a radially symmetric solution of the heat equation which satisfies u(¦x¦, 0)=0 for ¦x¦⩾R (or 0<¦x¦⩽R) and which is L2 in time. Then there is a constant A=A(N) such that if 00. Our results extend, simplify, and in the case N=1, sharpen the results of Carasso, who studied the one dimensional problem. (SIAM J. Appl. Math.,24 (1982).)Similar results are also obtained for certain second order elliptic boundary value problems in unbounded domains. An analog of the three lines theorem is an easy consequence of these results.