The stability of traveling wave solutions of parabolic equations

[摘要] A method for determining by inspection the stability or instability of any solution u(t,x) = ɸ(x-ct) of any smooth equation of the form u_t = f(u_(xx),u_x,u where ∂/∂a f(a,b,c) > 0 for all arguments a,b,c, is developed. The connection between the mean wavespeed of solutions u(t,x) and their initial conditions u(0,x) is also explored. Themean wavespeed results and some of the stability results are then extendedto include equations which contain integrals and also to include somespecial systems of equations. The results are applied to several physicalexamples.

[发布机构] University:California Institute of Technology;Department:Physics, Mathematics and Astronomy

[关键词] Applied Mathematics