Strong convergence of bounded sequences of solutions of porous medium equations (Q1978208)

The paper deals with the differential inclusion \((\beta (u))_t \ni \Delta u + g(x,t)\) on \(\Omega \times (0,T)\), where \(\beta \) is a maximal monotone graph. The equation is completed with boundary and initial conditions \(u=\varphi \). For sufficiently smooth data the \(L^2\)-gradient estimate of the solution is derived; the estimate is on the set where the solution is small. The estimate allows to show that approximating smooth solutions converge strongly to the weak solution. The theorem is illustrated by an example.