Makoto Mizuguchi

Numerical validation of blow-up solutions of ordinary differential equations

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 compactifications and the Lyapunov function validation method. The necessary criteria for this construction can be verified using interval arithmetic techniques. Some numerical examples are presented to demonstrate the applicability of our method.

Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains

This paper is concerned with an explicit value of the embedding constant from W1,q(Ω)

Sharp numerical inclusion of the best constant for embedding H 0 1 ( ź ) ź L p ( ź ) on bounded convex domain

W^{1,q}(\Omega)

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

to Lp(Ω)

A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory

L^{p}(\Omega)

Verified Computations for Solutions to Semilinear Parabolic Equations Using the Evolution Operator

for a domain Ω⊂RN

On the embedding constant of the Sobolev type inequality for fractional derivatives

\Omega\subset\mathbb{R}^{N}

Estimation of Sobolev-type embedding constant on domains with minimally smooth boundary using extension operator

(N∈N

Accurate method of verified computing for solutions of semilinear heat equations

N\in\mathbb{N}

Numerical validation of blow-up solutions for ODEs

), where 1≤q≤p≤∞