We consider the following quasilinear parabolic equation of degenerate type with convection term ut = φ (u)xx + b(u)x in (-L,0) x (0,T). We solve the associate initial-boundary data problem, with nonlinear flux conditions. This problem describes the evaporation of an incompressible fluid from a homogeneous porous media. The nonlinear condition in x = 0 means that the flow of fluid leaving the porous media depends on variable meteorological conditions and in a nonlinear manner on u. In x = -L we have an imprevious boundary. For a sufficiently smooth initial data, one proves the existence and uniqueness of the global strong solution in the class of bounded variation functions.
@article{urn:eudml:doc:41186,
title = {Existence and uniqueness of solutions for a degenerate quasilinear parabolic problem.},
journal = {Publicacions Matem\`atiques},
volume = {38},
year = {1994},
pages = {327-352},
mrnumber = {MR1316631},
zbl = {0830.35063},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41186}
}
Badii, Maurizio. Existence and uniqueness of solutions for a degenerate quasilinear parabolic problem.. Publicacions Matemàtiques, Tome 38 (1994) pp. 327-352. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41186/