@article{oai:tsukuba.repo.nii.ac.jp:00041683,
 author = {高安, 亮紀 and 久保, 隆徹 and Mizuguchi, Makoto and Takayasu, Akitoshi and Kubo, Takayuki and Oishi, Shin'ichi},
 issue = {2},
 journal = {SIAM journal on numerical analysis},
 month = {Apr},
 note = {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 from Banach's fixed-point theorem. This paper also introduces a recursive scheme to extend a time interval in which the validity of the solution can be verified. As an application of this method, the existence of a global-in-time solution is demonstrated for a certain semilinear parabolic equation.},
 pages = {980--1001},
 title = {A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory},
 volume = {55},
 year = {2017}
}