For an equation of the type of porous media equation the Cauchy-Dirichlet and Cauchy-Neumann problems are considered. The existence and uniqueness results in the case of initial and boundary data are given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-13, author = {Jan Goncerzewicz}, title = {On the initial-boundary value problems for a degenerate parabolic equation}, journal = {Banach Center Publications}, volume = {83}, year = {2008}, pages = {197-211}, zbl = {1154.35062}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-13} }
Jan Goncerzewicz. On the initial-boundary value problems for a degenerate parabolic equation. Banach Center Publications, Tome 83 (2008) pp. 197-211. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-13/