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

Publicacions Matemàtiques (1994)

- Volume: 38, Issue: 2, page 327-352
- ISSN: 0214-1493

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topBadii, 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 -

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