ON COMPUTATIONAL PROOFS OF THE EXISTENCE OF SOLUTIONS TO NONLINEAR PARABOLIC PROBLEMS

[摘要] This paper is an extension of the preceding study (Nakao, this journal, 1991) in which we described a numerical verification method of the solution for one-space dimensional parabolic problems, to the several-space dimensional case. Here, numerical verification means the automatic proof of the existence of solutions to the problems by some numerical techniques on a computer. We reformulate the verification condition for nonlinear parabolic initial boundary value problems using the fixed-point problem of a compact operator on certain function spaces. As in the preceding study based upon a simple C0 finite-element approximation and its constructive a priori error estimates, a numerical verification procedure is presented with some numerical examples.

[发布日期] 1994-05-20

[效力级别]  Proceedings Paper

[关键词] PARABOLIC PROBLEM;FINITE-ELEMENT METHOD;ERROR ESTIMATES;FIXED-POINT THEOREM