Convergence to equilibrium for parabolic-hyperbolic time-dependent Ginzburg-Landau-Maxwell equations

In this talk, I will first briefly introduce the Lojasiewicz–Simon approach in the study of longtime behavior of global solutions to nonlinear evolution equations. Then as an application, we study a parabolic-hyperbolic Ginzburg–Landau–Maxwell model, which describes the behavior of a two-dimensional superconducting material. We use the extended Lojasiewicz–Simon approach to show that for any initial datum in certain phase space, the corresponding global solution converges to an equilibrium as time goes to infinity. Besides, we also provide an estimate on the convergence rate with respect to the phase space metric.In this talk, I will first briefly introduce the Lojasiewicz–Simon approach in the study of longtime behavior of global solutions to nonlinear evolution equations. Then as an application, we study a parabolic-hyperbolic Ginzburg–Landau–Maxwell model, which describes the behavior of a two-dimensional superconducting material. We use the extended Lojasiewicz–Simon approach to show that for any initial datum in certain phase space, the corresponding global solution converges to an equilibrium as time goes to infinity. Besides, we also provide an estimate on the convergence rate with respect to the phase space metric.In this talk, I will first briefly introduce the Lojasiewicz–Simon approach in the study of longtime behavior of global solutions to nonlinear evolution equations. Then as an application, we study a parabolic-hyperbolic Ginzburg–Landau–Maxwell model, which describes the behavior of a two-dimensional superconducting material. We use the extended Lojasiewicz–Simon approach to show that for any initial datum in certain phase space, the corresponding global solution converges to an equilibrium as time goes to infinity. Besides, we also provide an estimate on the convergence rate with respect to the phase space metric.In this talk, I will first briefly introduce the Lojasiewicz–Simon approach in the study of longtime behavior of global solutions to nonlinear evolution equations. Then as an application, we study a parabolic-hyperbolic Ginzburg–Landau–Maxwell model, which describes the behavior of a two-dimensional superconducting material. We use the extended Lojasiewicz–Simon approach to show that for any initial datum in certain phase space, the corresponding global solution converges to an equilibrium as time goes to infinity. Besides, we also provide an estimate on the convergence rate with respect to the phase space metric.