Hysteresis in pde/ode

*To*: mathgroup at smc.vnet.net*Subject*: [mg79831] Hysteresis in pde/ode*From*: "jhelffrich at gmail.com" <jhelffrich at gmail.com>*Date*: Mon, 6 Aug 2007 03:36:05 -0400 (EDT)

I am trying to solve a two-space-dimensional and one time-dimension PDE for a displacement variable u(r,z) , something like c*d^2u/dt^2 = d^2(ru)/dr^2 + d^2u/dz^2 + f(u,t) where f(u,t) is a hysteresis term that accounts for the fact that if (du/dt) > its neighbor's values del^2(du/dt) < 0 then f=+1 and if del^2(du/dt) > 0 then f=-1. This is a sort of binary link with its neighbors. Are there any similar problems out there from which I might get some guidance for solving this numerically? Other than this, the problem is simple in that the boundary conditions are fixed values at finite distance. Thanks