Existence and uniqueness of solutions for a degenerate quasilinear parabolic problem.

Badii, Maurizio. "Existence and uniqueness of solutions for a degenerate quasilinear parabolic problem.." Publicacions Matemàtiques 38.2 (1994): 327-352. <http://eudml.org/doc/41186>.

@article{Badii1994,
abstract = {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.},
author = {Badii, Maurizio},
journal = {Publicacions Matemàtiques},
keywords = {Ecuaciones parabólicas; Ecuaciones diferenciales en derivadas parciales; Ecuaciones diferenciales no lineales; Problema de Cauchy; global strong solution; bounded variation functions},
language = {eng},
number = {2},
pages = {327-352},
title = {Existence and uniqueness of solutions for a degenerate quasilinear parabolic problem.},
url = {http://eudml.org/doc/41186},
volume = {38},
year = {1994},
}

TY - JOUR
AU - Badii, Maurizio
TI - Existence and uniqueness of solutions for a degenerate quasilinear parabolic problem.
JO - Publicacions Matemàtiques
PY - 1994
VL - 38
IS - 2
SP - 327
EP - 352
AB - 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.
LA - eng
KW - Ecuaciones parabólicas; Ecuaciones diferenciales en derivadas parciales; Ecuaciones diferenciales no lineales; Problema de Cauchy; global strong solution; bounded variation functions
UR - http://eudml.org/doc/41186
ER -