Results on a Mathematical Model of Thermomechanical Phase Transitions in Shape Memory Materials

RUBEN D. SPIES

Smart Materials and Structures

Institute of Physics

Lugar: London; Año: 1994 vol. 3 p. 459 - 469

0964-1726

Abstract. In this paper we prove the local existence of solutions for a mathematical model of structural phase transitions in solids with nonconvex Landau-Ginzburg free energy potentials. The partial differential equations that arise from the conservation laws of linear momentum and energy are sometimes referred to as the equations of thermo-visco-elasto-plasticity. The theory of real interpolation spaces for maximal accretive operators is used to show the well posedness of the system when the initial data are in the domain of the ( 3/4 + epsilon )-power of the associated linear differential operator. This not only improves previous existence results by weakening the assumptions on the initial data, but also allows us to obtain some regularity properties of the solutions. The fact that local existence is obtained for initial data in the domain of a fractional delta -power of the differential operator, with delta strictly less than unity, has several important implications for continuity with respect to the admissible parameters.