Unique global solvability of 1D Fried-Gurtin model

• Autorzy: Zenon Kosowski
• Języki publikacji: EN

Abstrakty

EN

We investigate a 1-dimensional simple version of the Fried-Gurtin 3-dimensional model of isothermal phase transitions in solids. The model uses an order parameter to study solid-solid phase transitions. The free energy density has the Landau-Ginzburg form and depends on a strain, an order parameter and its gradient. The problem considered here has the form of a coupled system of one-dimensional elasticity and a relaxation law for a scalar order parameter. Under some physically justified assumptions on the strain energy and data we prove the existence and uniqueness of a regular solution to the problem. The proof is based on the Leray-Schauder fixed point theorem.

Kategorie tematyczne

• 74B20: Nonlinear elasticity
• 35K60: Nonlinear initial value problems for linear parabolic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2007
• Tom: 34
• Numer: 3
• Strony: 269-288

Daty

wydano

2007

Twórcy

autor

Zenon Kosowski

• Institute of Mathematics and Cryptology, Faculty of Cybernetics, Military University of Technology, Kaliskiego 2, 00-908 Warszawa, Poland

Identyfikatory

DOI

10.4064/am34-3-2