An Exact Solution of the Reaction-Diffusion Equation for the Speed of the Interface Propagation in Superconductors
Keywords:Front propagation in superconductor; Ginzburg-Landau equation; velocity selection; exact solution
The speed of interface propagation in superconductors for the scalar reaction-diffusion equation ut = ∇2u+ F(u) is studied in detail. Here the non linear reaction term F (u) is the time-dependent Ginzburg-Landau or TDGL equation F(u)=u-u3 which describes the dynamics of the order-disorder transition. In contrast to what has been done in previous work  here an improved exact solution has derived by using TDGL equation to determine the speed of the front propagation. The analytical treatment of this study has been found in good agreement with the numerical simulation of V. Mendez et al.  and Di Bartolo and Dorsey .
The Chittagong Univ. J. Sci. 40(1) : 85-95, 2019
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