The existence of entropy solutions to some parabolic problems with \(L^1\) data (Q1601224)

The paper deals with the existence of entropy solutions in the sense of \textit{A. Prignet} [Nonlinear Anal., Theory Methods Appl. 28, 1943-1954 (1997; Zbl 0909.35075)] to the parabolic problem \[ \frac{\partial u}{\partial t}- \operatorname {div}(a(x,t,Du))+ \operatorname {div} \Phi (u)= f\quad\text{in }\Omega \times (0,T), \] \[ u=0 \quad\text{on }\partial \Omega \times (0,T),\qquad u(x,0) =u_{0}(x) \quad\text{in }\Omega . \] The data \(f,\) \(u_{0}\) belong to \(L^{1}\) and no growth assumption is made on the function \(\Phi .\)