Person:
Díaz Díaz, Jesús Ildefonso

First Name

Jesús Ildefonso

Last Name

Díaz Díaz

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Ciencias Matemáticas

Department

Análisis Matemático Matemática Aplicada

Area

Matemática Aplicada

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Now showing 1 - 10 of 230

On the Newton partially flat minimal resistance body type problems
(European Mathematical Society, 2005) Díaz Díaz, Jesús Ildefonso; Comte, M.
We study the flat region of stationary points of the functional integral(Omega) F(|del u(x)|) dx under the constraint u <= M, where Omega is a bounded domain in R-2. Here F( s) is a function which is concave for s small and convex for s large, and M > 0 is a given constant. The problem generalizes the classical minimal resistance body problems considered by Newton. We construct a family of partially flat radial solutions to the associated stationary problem when Omega is a ball. We also analyze some other qualitative properties. Moreover, we show the uniqueness of a radial solution minimizing the above mentioned functional. Finally, we consider nonsymmetric domains Omega and provide sufficient conditions which ensure that a stationary solution has a flat part.
Positive and Free Boundary Solutions to Singular Nonlinear Elliptic Problems with Absorption: An Overview and Open Problems
(Department of Mathematics Texas State University, 2014) Díaz Díaz, Jesús Ildefonso; Hernández, Jesús
We give a survey of recent results and open problems concerning existence and multiplicity of positive and/or compact support solutions to some semilinear elliptic equations with singular nonlinear terms of absorption type. This includes the case of discontinuous (at the origin) nonlinearities, which is treated by introducing maximal monotone graphs. Extensions to the p-Laplacian are also considered. The one-dimensional case is studied by using energy methods.
On a stochastic parabolic PDE arising in Climatology
(Springer, 2002) Díaz Díaz, Gregorio; Díaz Díaz, Jesús Ildefonso
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 balance climate models. The more delicate point concerns the uniqueness of solutions due to the presence of a multivalued graph β in the right hand side of the equation. In contrast with the deterministic case, it is possible to prove the uniqueness of a suitable weak solution associated to each given monotone (univalued and discontinuous) section b of the maximal monotone graph β. We get some stability results when the white noise converges to zero.
On the uniqueness of solutions of a nonlinear elliptic problem arising in the confinement of a plasma in a Stellarator device
(Akademie Verlag GMBH, 1996) Díaz Díaz, Jesús Ildefonso; Galiano, Gonzalo; Padial Molina, Juan Francisco
We obtain the uniqueness of solutions of a nonlocal elliptic problem when the nonlinear terms at the right hand side are assumed to be prescribed. The problem arises in the study of the magnetic confinement of a plasma in a Stellarator device.
The extinction versus the blow-up: Global and non-global existence of solutions of source types of degenerate parabolic equations with a singular absorption.
(Elsevier, 2017) Dao, A. N; Díaz Díaz, Jesús Ildefonso
We consider nonnegative solutions of degenerate parabolic equations with a singular absorption term and a source nonlinear term: partial derivative(t)u - (vertical bar u(x)vertical bar(P-2)u(x))(x) + u(-beta) X{u > 0} = f (u,x,t), in I x (0, T), with the homogeneous zero boundary condition on I = (x(1), x(2)), an open bounded interval in R. Through this paper, we assume that p > 2 and beta is an element of (0, 1). To show the local existence result, we prove first a sharp pointwise estimate for vertical bar u(x vertical bar) I. One of our main goals is to analyze conditions on which local solutions can be extended to the whole time interval t is an element of(0, infinity), the so called global solutions, or by the contrary a finite time blow-up tau(0) > 0 arises such that lim (t ->tau 0) vertical bar vertical bar u(t)vertical bar vertical bar(L infinity(I)) = +infinity. Moreover, we prove that any global solution must vanish identically after a finite time if provided that either the initial data or the source term is small enough. Finally, we show that the condition f (0, x, t) = 0, for all(x, t) is an element of I x (0, infinity) is a necessary and sufficient condition for the existence of solution of equations of this type.
Finite time extinction for nonlinear fractional evolution equations and related properties
(Texas State University, 2016) Díaz Díaz, Jesús Ildefonso; Pierantozzi, T.b; Vázquez, L.
The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly, we consider the limit case when only the fractional derivative remains. The latter is the most extraordinary case, since we prove that the finite time extinction phenomenon still appears, even with a non-smooth profile near the extinction time. Some concrete examples of quasi-linear partial differential operators are proposed. Our results can also be applied in the framework of suitable nonlinear Volterra integro-differential equations.
Free boundaries touching the boundary of the domain for some reaction-diffusion problems
(Elsevier, 2015-06) Díaz Díaz, Jesús Ildefonso; Mingazzini, Tommaso
We give conditions on the behaviour of the trace datum near the boundary of its support in order to know whether the free boundary given by the boundary of the support of the solution of suitable elliptic or parabolic semilinear problem is connected or not with the boundary of the support of the boundary datum.
Homogenization of the p-Laplacian with nonlinear boundary condition on critical size particles: Identifying the strange term for the some non smooth and multivalued operators
(Maik Nauka-Interperiodica Publishing, 2016) Díaz Díaz, Jesús Ildefonso; Gómez de Castro, Ana Inés; Podol’skii, A. V.; Shaposhnikova, T.A.
We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involving some maximal monotone graphs which may correspond to discontinuous or non-Lipschitz functions arising in some catalysis problems.
On the Boussinesq system with non linear thermal diffusion
(Elsevier, 1997-12) Díaz Díaz, Jesús Ildefonso; Galiano, Gonzalo
The Boussinesq system of hydrodynamics equations, arises from a zero order approximation to the coupling between the Navier-Stokes equations and the thermodynamic equation. The presence of density gradients in a fluid means that gravitational potential energy can be converted into motion through the action of bouyant forces.
On the free boundary for quenching type parabolic problems via local energy methods
(American Institute of Mathematical Sciences, 2014) Díaz Díaz, Jesús Ildefonso
We extend some previous local energy method to the study the free boundary generated by the solutions of quenching type parabolic problems involving a negative power of the unknown in the equation.