Nakao, Mitsuhiro T.; Hashimoto, Kouji A numerical verification method for solutions of nonlinear parabolic problems. (English) Zbl 1211.35153 J. Math-for-Ind. 1, No. A, 69-72 (2009). Summary: 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. Cited in 4 Documents MSC: 35K58 Semilinear parabolic equations 35K20 Initial-boundary value problems for second-order parabolic equations 35A35 Theoretical approximation in context of PDEs 35A01 Existence problems for PDEs: global existence, local existence, non-existence 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 35B45 A priori estimates in context of PDEs Keywords:linearized inverse operator; Newton-type operator; Schauder’s fixed point theorem PDFBibTeX XMLCite \textit{M. T. Nakao} and \textit{K. Hashimoto}, J. Math-for-Ind. 1, No. A, 69--72 (2009; Zbl 1211.35153) Full Text: Link