Existence for one-dimensional nonlinear parabolic Volterra integrodifferential equations (Q1801438)

In this note, the authors consider global solvability of the nonlinear integrodifferential equation: \(u_ t=a(x,t,u,u_ x)u_{xx}+b(x,t,u,u_ x)+\int^ t_ 0c(x,t,\tau,u,u_ x,u_{xx})d\tau\) subject to appropriate initial and boundary conditions, under suitable assumptions concerning the data and the functions \(a,b\) and \(c\).