The paper is devoted to the study of the homogeneous Dirichlet problem for the doubly nonlinear parabolic equation with nonstandard growth conditions: ut = div ( a(x, t, u)|u|α(x,t)|∇u|p(x,t)−2∇u)+ f… (More)

We study the homogeneous Dirichlet problem for the equation ut = n ∑ i=1 Di ( ai|Di(|u|m(x)−1u)|pi(x,t)−2Di(|u|m(x)−1u) ) +b|u|σ(x,t)−2u with given exponents m(x) , pi(x,t) and σ(x,t) . It is proved… (More)

We study the boundary layer approximation of the, already classical, mathematical model which describes the discharge of a laminar hot gas in a stagnant colder atmosphere of the same gas. We start by… (More)

This work deals with the study of a compactness result for a class of pseudoparabolic problems of type: ∂tu− div{a(∂tu+ E)∇(u+ τ∂tu)} = 0. with boundary conditions that takes explicitly into account… (More)

We consider a general class of one-dimensional parabolic systems, mainly coupled in the diffusion term, which, in fact, can be of the degenerate type. We derive some new L1-gradient type estimates… (More)

L’accès aux archives de la revue « Annales de la faculté des sciences de Toulouse » (http://picard.ups-tlse.fr/~annales/) implique l’accord avec les conditions générales d’utilisation… (More)

We prove local existence of classical solutions to the well-posed Hele–Shaw problem under general conditions on the fixed boundaries. Our approach consists of a construction of approximate solutions… (More)