Mitsuhiro T. Nakao and Yoshitaka Watanabe:

On Computational Proofs of the Existence of Solutions to Nonlinear
Parabolic Problems,

*Journal of Computational and Applied Mathematics* 50
(1994) pp.401-410.

( Modern Language Association of America style )

Nakao, M.T. and Y. Watanabe.
"On Computational Proofs of the Existence of Solutions to Nonlinear
Parabolic Problems."
*J. Comput. Appl. Math.* 50 (1994) 401-410.

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, the 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 C^0 finite element approximation and its constructive a priori error estimates, a numerical verification procedure is presented with some numerical examples. 10 pages.

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