## JMI2009A-9 A numerical verification method for solutions of nonlinear parabolic problems (pp.69-72)

Author(s)： Mitsuhiro T. Nakao and Kouji Hashimoto

J. Math-for-Ind. 1A (2009) 69-72.

Abstract
By using the finite element approximation and constructive a priori error estimates, a new formulation for proving the existence of solutions for nonlinear parabolic problems is presented. We present a method to estimate the norm of the linearized inverse operator for concerned nonlinear problem. Then we formulate a verification principle for solutions by using the Newton-type operator incorporating with Schauder's fixed point theorem.

Keyword(s).　 Numerical veriﬁcation, Guaranteed error bounds, Parabolic problem