Hattori 9704383 We discuss the three subjects that are related to materials science. They are the phase transition problem, magnetostriction, and hydrodynamic models of semiconductors. The phase transition problems are a fundamental problem in physics and an important research area in engineering. Some of the materials undergoing the phase transition are called ``smart materials.'' Typical examples are shape memory alloys. In the phase transition problem we examine the compatibility of the entropy rate admissibility criterion and the entropy condition. Then, we discuss the existence of global weak solutions and numerical analysis. We need a careful analysis of the interaction between phase boundary and elementary waves (shock waves and rarefaction waves). I believe that this research will bring a better understanding of the phase transitions. The magnetostriction is the combination of wave equations for elasticity and the Landau-Lifshitz equations for the magnetic moment. We can regard them as nonlinear wave equations with rate equations, where the rate equations have a special structure. This gives an interesting dynamics. We consider the traveling wave solutions, the smooth and weak solutions, numerical analysis, and etc. We also consider the Ericksen bar. Some magnetic materials undergo phase transition. This research may bring an insight to it. Also, this research may be useful to study the hysteretic behavior observed in some magnetic materials. The semiconductors are important materials or devices in industry. Recently, the hydrodynamic models are becoming more popular. The equations we discuss consist of the hydrodynamic equations for electrons and the Poisson equation for the electrostatic potential. We consider mainly the stability of steady state solutions. The stability issue is an important subject especially when there are multiple steady state solutions. I study mathematical aspects of materials science. One goal is to have better understanding of t he phase transitions. In phase transition problems we discuss the change of various properties of materials due to change in factors such as temperature. A typical example is water which changes to vapor or ice depending on temperature. The phase transitions take place in magnetic materials too. The phase transitions in magnetic materials are used for various switching devices or recording devices. A very good example of magnetic material is a videorecording tape. It is important to understand the mechanisms of phase transitions so that we can construct better devices. In some such materials, it is important to consider both elastic and magnetic effects as both influence the ways in which the phase transitions occurs. By elastic effects we mean the effects associated with compressing or pulling the material. There are mathematical models describing the phase transitions. I plan to study how various effects such as above influence each other. I would like to study these mathematical models analytically as well as numerically. I also study hydrodynamic models of semiconductors. In these types of models we regard the electric current as ``fluid'' and study how this ``fluid'' flows in semiconductors. Semiconductors are used in PCs and other electric devices. To study how the electric current runs in the semiconductors is very important and interesting. There are a few hydrodynamic models depending on what kind of effects one wants to consider. An important effect that has not been considered is temperature. I would like to consider such effects.
