Existense, Uniqueness Of Traveling Wave Solutions Of Some Intrgral Differential Equations Arising Frome Neuronal Networks

In this paper, the existence and uniqueness of traveling wavesolutions of the integral differential equations:u_t=f(u,w)+αintegral from R(K(x-y)H(u(y,t)-θ)dy)were studied. The strategy to solve this problem is to transformthe equations to autonomous ordinary differential equations. Thenby using the qualitative technique for plane autonomous system,the existence and uniqueness of traveling wave were proved. Then,the properties of the solutions of the equations were studied.