The Classical Solutions to a Cauchy Problem of Parabolic Type Coupled with Operators (Journal of Partial Differential Equations, 2020)
"We consider the equation u_t = Tr[B(x, t, Du, \u03a6u)D\u00b2u] + F(x, t, u, Du, \u03a6u, \u03c8u) where \u03a6 and \u03c8 are vector-valued mappings. We obtain the existence and uniqueness of classical solution to the equation for a \u2208- periodic initial data. The problem is naturally arisen from image denoising."