Akitoshi Takayasu

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  An approach for verified computations of semilinear parabolic equations using the semigroup theory
  Akitoshi Takayasu

  For an initial-boundary value problem of semilinear parabolic equations, a computational method is proposed to rigorously prove that the exact solution is enclosed in a ball. Central to our method is to use the semigroup theory with fully discretized approximations organized by Galerkin method and the backward Euler method, which is the most elementary scheme for parabolic equations. Using the scheme as it is, a step-by-step approach has been investigated. Our method is capable of verifying the weak solutions by using the Galerkin method.

  
  

  It implies that the domain is allowed to be a polygonal or polyhedral domain with arbitrary shape. This work is joint with Mr. Makoto Mizuguchi, Dr. Takayuki Kubo, and Prof. Shin'ichi Oishi