Renormalized solutions to a parabolic equation with mixed boundary constraints
Tan Duc, Le Xuan Truong, Nguyễn Ngọc Trọng · Dissertationes Mathematicae · 2024
We establish the existence and uniqueness of a renormalized solution to the parabolic equation \[ \frac{\partial b(u)}{\partial t} - \mathop{\rm div}(a(x,t,u, abla u)) = f \quad\ \mbox{in } \Omega\times(0,T) \] subject to a mixed boundary condition.