Shoji Yotsutani

Semilinear elliptic equations of Matukuma-type and related topics

We investigate the structure of solutions of some semilinear elliptic equations, which include Matukuma’s equation as a special case. It is a mathematical model proposed by Matukuma, an astrophysicist, in 1930 to describe the dynamics of a globular cluster of stars. Equations of this kind have come up both in geometry and in physics, and have been a subject of extensive studies for some time. However, almost all the methods previously developed do not seem to apply to the original Matukuma’s equation. Our results cover most of the cases left open by previous works.

Stefan problems with the unilateral boundary condition on the fixed boundary. II

On considere des problemes de Stefan a 1 phase a 1 dimension avec la condition limite unilaterale sur la frontiere fixee

Global structure of solutions for equations of Brezis-Nirenberg type on the unit ball

The Brezis-Nirenberg equation and the scalar field equation on the three-dimensional unit ball are studied. Under the Robin condition, we show the existence and uniqueness of radial solutions in a unified way. In particular, it is shown that the global structure of solutions changes qualitatively when a parameter in the boundary condition exceeds a certain critical value.

A unified approach to the structure of radial solutions for semilinear elliptic problems

Radial solutions of semilinear elliptic problems satisfy some boundary value problems for second order differential equations. It is shown that the boundary value problems can be reduced to a canonical form after suitable change of variables. Through the canonical form, we can study the properties of radial solutions of semilinear elliptic equations in a systematic way, and make clear unknown structure of various equations. We also clarify the implication of the Kelvin transformation and the Rellich-Pohozaev identity, and give their generalized forms.

Global bifurcation structure of a one-dimensional Ginzburg–Landau model

We consider an equation of a simplified Ginzburg–Landau model of superconductivity in a one-dimensional ring. The equation for a complex order parameter ψ has two real parameters μ and λ related to the magnitude of an applied magnetic field and the Ginzburg–Landau parameter, respectively. The purpose of this paper is to reveal a global bifurcation structure for the equation in the parameter space (μ,λ). In particular we show that there exist modulating amplitude solutions which bifurcate from constant amplitude solutions, and how the bifurcation branches of such solutions continue or disappear as μ varies. We also determine the minimizer of the energy functional.

A mathematical model on chemical interfacial reactions

This paper discusses a sort of parabolic system with nonlinear boundary conditions, which comes from the chemical interfacial models. The results obtained here are the uniqueness and the existence of the global solutions.

On a Free Boundary Problem in Ecology

This article is concerned with a free boundary problem for semilinear parabolic equations, which describes the habitat segregation phenomenon in population ecology. The main purpose is to show the global existence, uniqueness, regularity and asymptotic behavior of solutions for the problem. The asymptotic stability or instability of each solution is completely determined using the comparison theorem.