11 citations · 13 across the 5 of their papers we have counts for
5 papers
Accurate method of verified computing for solutions of semilinear heat equations
Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo +1
We provide an accurate verification method for solutions of heat equations with a superlinear nonlinearity. The verification method numerically proves the existence and local uniqu…
Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains
Makoto Mizuguchi, Kazuaki Tanaka, Kouta Sekine +1
This paper is concerned with an explicit value of the embedding constant from to for a bounded domain , where $1\leq…
Numerical validation of blow-up solutions of ordinary differential equations
Akitoshi Takayasu, Kaname Matsue, Takiko Sasaki +3
This paper focuses on blow-up solutions of ordinary differential equations (ODEs). We present a method for validating blow-up solutions and their blow-up times, which is based on c…
Sharp numerical inclusion of the best constant for embedding on bounded convex domain
Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi +1
In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding on bounded conv…
Estimation of the Sobolev embedding constant on domains with minimally smooth boundary
Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi +1
In this paper, we propose a method for estimating the Sobolev type embedding constant on a domain with minimally smooth boundary. We estimate the embedding constant by constructing…