# A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory

@article{Mizuguchi2017AMO, title={A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory}, author={Makoto Mizuguchi and Akitoshi Takayasu and Takayuki Kubo and Shin'ichi Oishi}, journal={SIAM J. Numer. Anal.}, year={2017}, volume={55}, pages={980-1001} }

This paper presents a numerical method for verifying the existence and local uniqueness of a solution for an initial-boundary value problem of semilinear parabolic equations. The main theorem of this paper provides a sufficient condition for a unique solution to be enclosed within a neighborhood of a numerical solution. In the formulation used in this paper, the initial-boundary value problem is transformed into a fixed-point form using an analytic semigroup. The sufficient condition is derived…

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