46 citations · 50 across the 8 of their papers we have counts for
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New definitions of a solution of a one-dimensional elliptic equation with a singular first order divergence term
Daniela Giachetti, Pedro Jesús Martínez-Aparicio, François Murat +1
In this paper, which is a continuation of our recent paper [1], we give two new definitions of a weak solution of the one-dimensional, elliptic, nonlinear singular problem which is…
An intrinsic Proper Generalized Decomposition for parametric symmetric elliptic problems
M. Azaïez, F. Ben Belgacem, J. Casado-Díaz +2
We introduce in this paper a technique for the reduced order approximation of parametric symmetric elliptic partial differential equations. For any given dimension, we prove the ex…
Definition, existence, stability and uniqueness of the solution to a semilinear elliptic problem with a strong singularity at
Daniela Giachetti, Pedro J. Martínez-Aparicio, François Murat
In this paper we consider a semilinear elliptic equation with a strong singularity at , namely $ \displaystyle u\geq 0 \mbox{ in } Ω$, $ \displaystyle - div \,A(x) D u = F(x,u…
Quasilinear problems involving a perturbation with quadratic growth in the gradient and a noncoercive zeroth order term
Boussad Hamour, François Murat
In this paper we consider the problem u in H^1_0 (Omega), - div (A(x) Du) = H(x, u, Du) + f(x) + a_0 (x) u in D'(Omega), where Omega is an open bounded set of R^N, N \geq 3, A(x) i…
A semilinear elliptic equation with a mild singularity at : existence and homogenization
Daniela Giachetti, Pedro J. Martínez-Aparicio, François Murat
In this paper we consider semilinear elliptic equations with singularities, whose prototype is the following \begin{equation*} \begin{cases} \displaystyle - div \,A(x) D u = f(x)g(…
Asymptotic behavior of an elastic beam fixed on a small part of one of its extremities
Juan Casado-Diaz, Manuel Luna-Laynez, Francois Murat
We study the asymptotic behavior of the solution of an anisotropic, heterogeneous, linearized elasticity problem in a cylinder whose diameter tends to zero. The cylinder is ass…