In this paper, a mathematical analysis of in-situ biorestoration is presented. Mathematical formulation of such process leads to a system of non-linear partial differential equations coupled with ordinary differential equations. First, we introduce a notion of weak solution then we prove the existence of at least one such a solution by a linearization technique used in Fabrie and Langlais (1992). Positivity and uniform bound for the substrates concentration is derived from the maximum principle while some regularity properties, for the pressure and velocity, are obtained from a local Meyers lemma (Bensoussan et al (1978), Meyers (1963)). Next, assuming some regularity on the solution, an uniqueness result is presented. Asymptotical behavior for the contaminant is also studied.
@article{urn:eudml:doc:44235,
title = {Approximation of the viscosity solution of a Hamilton-Jacobi problem. },
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {9},
year = {1996},
pages = {393-433},
zbl = {0873.35042},
mrnumber = {MR1430787},
language = {fr},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44235}
}
Fabrie, P.; Rasetarinera, P. Approximation of the viscosity solution of a Hamilton-Jacobi problem. . Revista Matemática de la Universidad Complutense de Madrid, Tome 9 (1996) pp. 393-433. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44235/