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

  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.},
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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