TY - JOUR
T1 - The Classical Solutions to a Cauchy Problem of Parabolic Type Coupled with Operators
JO - Journal of Partial Differential Equations
VL - 4
SP - 303
EP - 315
PY - 2004
DA - 2004/11
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5395.html
KW - ∈- periodic
KW - degenerate parabolic
KW - regularization
KW - image denoising
AB - 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.