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Artículo
On the existence and multiplicity of positive solutions for some indefinite nonlinear eigenvalue problem
(American Mathematical Society, 2004-06)
This paper concerns with the existence, uniqueness and/or multiplicity, and stability of positive solutions of an indefinite weight elliptic problem with concave or convex nonlinearity. We use mainly bifurcation method to ...
Artículo
On the controllability of the heat equation with nonlinear boundary Fourier conditions
(Elsevier, 2004-01-20)
In this paper we analyze the approximate and null controllability of the classical heat equation with nonlinear boundary conditions of the form ∂y ∂n + f(y) = 0 and distributed controls, with support in a small set. We ...
Artículo
Nonnegative solutions for a heterogeneous degenerate competition model
(Cambridge University Press, 2004-10)
This paper deals with the existence, uniqueness and qualitative properties of nonnegative and nontrivial solutions of a spatially heterogeneous Lotka-Volterra competition model with nonlinear diffusion. We give conditions ...
Artículo
Optimality conditions for nonconvex multistate control problems in the coefficients
(Society for Industrial and Applied Mathematics, 2004)
The purpose of this paper is to attain some optimality conditions for the identification of a diffusion matrix (material) under several restrictions. Assuming that the set of such diffusion matrices is closed for the ...
Artículo
Combining fast, linear and slow diffusion
(Juliusz Schauder Center for Nonlinear Studies, 2004)
Although the pioneering studies of G. I. Barenblatt ([8] G. I. Barenblatt, On some unsteady motions of a liquid or a gas in a porous medium, Prikl. Mat. Mekh. 16 (1952), 67–68) and A. G. Aronson and L. A. Peletier ([7] ...
Artículo
An eigenvalue problem for non-bounded quasi-linear operator
(Cambridge University Press, 2004-06)
In this paper we study the eigenvalues associated with a positive eigenfunction of a quasilinear elliptic problem with a not necessarily bounded operator. For that, we use the bifurcation theory and obtain the existence ...
Artículo
Combining linear and nonlinear diffusion
(De Gruyter, 2004-08)
In this paper we study a generalized porous medium equation where the diffusion rate, say m(x) —spatially heterogeneous—, is assumed to be linear, m = 1, on a piece of the support domain, Ω1, and slow nonlinear, m(x) > 1, ...
Artículo
Insensitizing controls for a heat equation with a nonlinear term involving the state and the gradient
(Elsevier, 2004)
In this paper we present two results on the existence of insensitizing controls for a heat equation in a bounded domain of IRN . We first consider a semilinear heat equation involving gradient terms with homogeneous Dirichlet ...