# Sur un problème parabolique-elliptique

Philippe Benilan; Petra Wittbold

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 1, page 121-127
- ISSN: 0764-583X

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topBenilan, Philippe, and Wittbold, Petra. "Sur un problème parabolique-elliptique." ESAIM: Mathematical Modelling and Numerical Analysis 33.1 (2010): 121-127. <http://eudml.org/doc/197388>.

@article{Benilan2010,

abstract = {
We prove existence (uniqueness is easy) of a weak solution to a boundary value problem for an equation like $(v-1)^+_t = v_\{xx\} + F(v)_x$ where the function $F: \Bbb R\rightarrow\Bbb R$ is only
supposed to be locally lipschitz continuous. In order to replace the lack of compactness in t on v<1, we use nonlinear semigroup theory.
},

author = {Benilan, Philippe, Wittbold, Petra},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {lack of compactness in },

language = {fre},

month = {3},

number = {1},

pages = {121-127},

publisher = {EDP Sciences},

title = {Sur un problème parabolique-elliptique},

url = {http://eudml.org/doc/197388},

volume = {33},

year = {2010},

}

TY - JOUR

AU - Benilan, Philippe

AU - Wittbold, Petra

TI - Sur un problème parabolique-elliptique

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 33

IS - 1

SP - 121

EP - 127

AB -
We prove existence (uniqueness is easy) of a weak solution to a boundary value problem for an equation like $(v-1)^+_t = v_{xx} + F(v)_x$ where the function $F: \Bbb R\rightarrow\Bbb R$ is only
supposed to be locally lipschitz continuous. In order to replace the lack of compactness in t on v<1, we use nonlinear semigroup theory.

LA - fre

KW - lack of compactness in

UR - http://eudml.org/doc/197388

ER -

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