A numerical verification method for solutions of nonlinear parabolic problems

Mitsuhiro T. Nakao
Kouji Hashimoto

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.

Journal of Math-for-industry

Faculty of Mathematics, Kyushu University

http://ci.nii.ac.jp/naid/120001177120
http://ci.nii.ac.jp/ncid/AA12444018
http://id.ndl.go.jp/bib/10948582
http://hdl.handle.net/2324/13976