Toyohiko Aiki

Weak solutions for Falk's model of shape memory alloys

In this paper we discuss the system of two partial differential equations governing the dynamics of phase transitions in shape memory alloys. We consider the one-dimensional model proposed by Falk, in which a term containing a fourth-derivative appears. The main purpose is to show the uniqueness for weak solutions of the problem by using the approximate dual equations for the system without growth condition for the free energy function. Copyright

A Prey-Predator Model with Hysteresis Effect

This paper provides mathematical analysis of a system of nonlinear PDEs which describes a prey-predator model with hysteresis effect. Existence and uniqueness of solutions for the system under consideration are proved.

A free-boundary problem for concrete carbonation : rigorous justification of the

A free-boundary problem for concrete carbonation : Front nucleation and rigorous justification of the root t-law of propagation

\sqrt t

AbstractWe consider one-phase Stefan problems for the equationui =uxx +u1+a (α>0)in one-dimensional space, which have blow-up solutions for a larger initial data. In this paper, the global existence result for our problem is proved by using energy inequalities. More precisely, if α>1 an initial function is sufficiently small, then the free boundary is bounded and

Global existence of solutions to one-phase Stefan problems for semilinear parabolic equations

|u(t)|_{L^\infty }

Blow-up points to one phase Stefan problems with Dirichlet boundary conditions

decay in exponential order.

Multiscale model for moisture transport with adsorption phenomenon in concrete materials

In our previous works we have proposed a mathematical model for dynamics of shape memory alloy materials. In the model the relationship between the strain and the stress is given as the generalized stop operator described by the ordinary differential equation including the subdifferential of the indicator function for the closed interval depending on the temperature. Here, we adopt the Duhem type of hysteresis operators as the mathematical description of the relationship in order to deal with the more realistic mathematical model. The aims of this paper are to show our new model and to establish the well-posedness of the model.

Relaxation for a Control Problem in Concrete Carbonation Modeling

We study one-phase Stefan problems for semilinear parabolic equations with Dirichlet boundary conditions in one-dimensional space. We show behavior of free boundaries of blow-up solutions at finite blow-up time and numerical experiments for our problem.