Continuous dependence for certain degenerate parabolic equations (Q1104480)

Let \(\Omega\) be an open and bounded subset of \({\mathbb{R}}^ d\) with sufficiently smooth boundary. The author considers the problem of finding time-periodic solutions for the parabolic equation \[ u_ t-\nabla \cdot \gamma (\cdot,| \nabla u|)\nabla u=f\quad in\quad [0,T]\times \Omega \] with an appropriate boundary condition, where \(\gamma\) may have an initial interval of degeneracy: \(\gamma (\cdot,r)=0\) for \(0\leq r\leq r_ 0\). The main result of the paper asserts that \(\gamma\) (\(\cdot,| \nabla u|)\nabla u\) depends continuously on f, \(\gamma\) and the boundary datum.