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Autor Díaz Díaz, Jesús Ildefonso |
Documentos disponibles escritos por este autor (214)
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We consider the nonlinear Schrodinger equation associated to a singular potential of the form a vertical bar u vertical bar(-(1-m))u + bu, for some In is an element of (0, 1), on a possible unbounded domain. We use some suitable energy methods t[...]![]()
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This paper is a review of recent results (including the author's work) on a two-dimensional free-boundary problem, modeling magnetohydrodynamic equilibrium in a stellarator nuclear fusion device. The main tools used in the paper under review are[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Lerena Guil, María Belen ; Padial Molina, Juan Francisco | Elsevier Science Ltd | 2002An initial-boundary value problem for the nonlinear elliptic–parabolic equation (_(u))t ?_u = G(u)(t, x)+J(u)(t, x) is considered. Here _(s) = min(s, 0) = ?s?, G and J are nonlocal operators. This problem arises in the study of magnetic confinem[...]![]()
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We prove the existence and some qualitative properties of the solution to a two-dimensional free-boundary problem modeling the magnetic confinement of a plasma in a Stellarator configuration. The nonlinear elliptic partial differential equation [...]![]()
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We study the rigidification phenomenon for several thin slender bodies or shells, with a small curvature in the transversal direction to the main length, for which the propagation of singularities through the characteristics is of parabolic type[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Galiano, Gonzalo ; Jungel, Ansgar | Pergamon Elsevier Science Ltd | 1999-06-01The temporal and spatial localization of vacuum sets of the solutions to the drift-diffusion equations for semiconductors is studied in this paper. It is shown that if there are vacuum sets initially then there are vacuum sets for a small time, [...]![]()
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Díaz Díaz, Jesús Ildefonso ; Galiano, Gonzalo ; Jungel, Ansgar | Pergamon Elsevier Science Ltd. | 2001-09This paper is about the drift-diffusion equations for semiconductors. Existence and uniqueness of weak solutions are obtained. The existence is proved by using the regularization technique. The proof of the uniqueness is interesting.![]()
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We study the rigidification phenomenon for several thin slender bodies or shells, with a small curvature in the transversal direction to the main length, for which the propagation of singularities through the characteristics is of parabolic type[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Padial Molina, Juan Francisco ; Rakotoson, Jean Michel Theresien | Cambridge University Press | 2007-09-18We consider some Bernoulli free boundary type problems for a general class of quasilinear elliptic (pseudomonotone) operators involving measures depending on unknown solutions. We treat those problems by applying the Ambrosetti-Rabinowitz minima[...]![]()
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It is known that several features of many react ion-diffusion systems can be studied through an associated Complex Ginzburg-Landau Equation (CGLE). In particular, the study of the catalytic CO oxidation leads to the Krischer-Eiswirth-Ertl model,[...]![]()
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We study the existence and uniqueness of solutions of a nonlinear stochastic pde proposed by R. North and R. F. Cahalan in 1982 for the modeling of non-deterministic variability (as, for instance, the volcano actions) in the framework of energy [...]![]()
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An ambiguity in the mathematical treatment of the study of bound state solutions of the Schrödinger equation for infinite well type potentials (studied for the first time in a pioneering article of 1928 by G. Gamow) is pointed out. An alternativ[...]![]()
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Sire prove the approximate controllability property for some higher order parabolic nonlinear equations of Cahn-Hilliard type when the nonlinearity is of sublinear type at infinity. We also give a counterexample showing that this property may fa[...]![]()
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In this communication we develop and improve some of the results of [4] on the approximate controllability of several semilinear parabolic boundary value problems where the nonlinear term appears either at the second order parabolic equation or [...]![]()
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We consider in this paper distributed systems governed by parabolic evolution equations which can blow up in finite time and which are controlled by initial conditions. We study here the following question : Can one choose the initial condition [...]