This article presents a theorem for guaranteeing existence of a solution for an initial-boundary value problem of semilinear parabolic equations. The sufficient condition of our main theorem is derived by a fixed-point formulation using the evolution operator. We note that the sufficient condition can be checked by verified numerical computations.
['Akitoshi Takayasu', 'Makoto Mizuguchi', 'T. Kubo', 'Shin’ichi Oishi']
Verified Computations for Solutions to Semilinear Parabolic Equations Using the Evolution Operator