Numerical verification for existence of a global-in-time solution to semilinear parabolic equations

This paper presents a method of numerical verification for existence of a global-in-time solution to a class of semilinear parabolic equations. Such a method is based on two main theorems in this paper. One theorem gives a sufficient condition for proving existence of a solution to the semilinear parabolic equations with the initial point t = t′ ≥ 0. If the sufficient condition does not hold, the other theorem is used for enclosing the solution for time t ∈ (0, τ ], τ > 0 in a neighborhood of a numerical solution. Numerical results of obtaining a global-in-time solution for a certain semilinear parabolic equation are also given.