Global smooth solutions for a class of parabolic integrodifferential equations
Hans Engler · Transactions of the American Mathematical Society · 1996
The existence and uniqueness of smooth global large data solutions of a class of quasilinear partial integrodifferential equations in one space and one time dimension are proved, if the integral kernel behaves like t − α t^{-\alpha } near t = 0 t=0 with α > 2 / 3 \alpha > 2/3 . An existence and regularity theorem for linear equations with variable coefficients that are related to this type is also proved in arbitrary space dimensions and with no restrictions for α \alpha .