The Classical Solutions to a Cauchy Problem of Parabolic Type Coupled with Operators

Abstract

"

We consider the equation u_t = Tr[B(x, t, Du, Φu)D²u] + F(x, t, u, Du, Φu, ψu) where Φ and ψ are vector-valued mappings. We obtain the existence and uniqueness of classical solution to the equation for a ∈- periodic initial data. The problem is naturally arisen from image denoising.<\/p>"