Homogenization in chemical reactive flows.
Conca, Carlos; Díaz, Jesus Ildefonso; Liñán, Amable; Timofte, Claudia — 2004
Electronic Journal of Differential Equations (EJDE) [electronic only]
Homogenization in chemical reactive flows.
An abstract approximate controllability result and applications to elliptic and parabolic systems with dynamic boundary conditions.
Two problems in homogenization of porous media.
The main goal of this work is to present two different problems arising in Fluid Dynamics of perforated domains or porous media. The first problem concerns the compressible flow of an ideal gas through a porous media and our goal is the mathematical derivation of Darcy's law. This is relevant in oil reservoirs, agriculture, soil infiltration, etc. The second problem deals with the incompressible flow of a fluid reacting with the exterior of many packed solid particles. This is related with absorption...
On the von Neumann problem and the approximate controllability of Stackelberg-Nash strategies for some environmental problems.
Two problems arising in Environment are considered. The first one concerns a conjecture posed by von Neumann in 1955 on the possible modification of the albedo in order to control the Earth surface temperature. The second one is related to the approximate controllability of Stackelberg-Nash strategies for some optimization problems as, for instance, the pollution control in a lake. The results of the second part were obtained in collaboration with Jacques-Lois Lions.
A variant of the Smale's model for flocks formation.
Soluciones con soporte compacto para ciertos problemas semilineales.
In this paper we prove that some classes of semilinear elliptic problems, formulated in very general terms by using the theory of maximal monotone graphs, admit a finite propagation speed. More concretely we show that if the data of these problems have compact supports, then the same happens to their solutions. These same thechniques will also be applied to some evolution problems. The first results in this direction are due to H. Brézis and to O. Oleinik & A. S. Kalashnikov & C. Yuilin...
On the asymptotic behavior for a damped oscillator under a sublinear friction.
Mostramos la existencia de dos curvas de datos iniciales (x, v) para las cuales las soluciones x(t) correspondientes del problema de Cauchy asociado a la ecuación x + |x| x + x = 0, supuesto α ∈ (0,1), se anulan idénticamente después de un tiempo finito. Mediante métodos asintóticos y argumentos de comparación mostramos que para muchos otros datos iniciales las soluciones decaen a 0, en un tiempo infinito, como t.
The waiting time property for parabolic problems trough the nondiffusion of support for the stationary problems.
In this note we study the waiting time phenomenon for local solutions of the nonlinear diffusion equation through its connection with the nondiffusion of the support property for local solutions of the family of discretized elliptic problems. We show that, under a suitable growth condition on the initial datum near the boundary of its support, a finite part of the family of solutions of the discretized problem maintain unchanged its support.
On a stochastic parabolic PDE arising in climatology.
Estudiamos la existencia y unicidad de soluciones de una ecuación estocástica en derivadas parciales de tipo parabólico propuesta por R. North y R. F. Cahalan en 1982 para la modelización de variabilidad no determinista (como es el caso, por ejemplo, de la acción de volcanes) en el marco de los modelos de balance de energía. El punto más delicado se refiere a la unicidad de soluciones debido a la presencia de un grafo multívoco β en el término de la derecha de la ecuación. En contraste con el caso...
Uniqueness of the boundary behavior for large solutions to a degenerate elliptic equation involving the ∞-Laplacian.
En esta nota estimamos la tasa máxima de crecimiento en la frontera de las soluciones de viscosidad de -Δ∞u + λ|u|m-1u = f en Ω (λ > 0, m > 3). De hecho, mostramos que sólo hay una única tasa de explosión en la frontera para esas soluciones explosivas. También obtenemos una versión del Teorema de Liouville para el caso Ω = RN.
Actions on environment under uncertainty: stochastic formulation and the associated deterministic problem.
Uniqueness of very singular self-similar solution of a quasilinear degenerate parabolic equation with absorption.
We show the uniqueness of the very singular self-similar solution of the equation ut - Δ pum + uq = 0. The result is carried out by studying the stationary associate equation and by introducing a suitable change of unknown. That allows to assume the zero-order perturbation term in the new equation to be monotone increasing. A careful study of the behaviour of solutions...
Uniqueness and existence of solution in the BV(Q) space to a doubly nonlinear parabolic problem.
In this paper we present some results on the uniqueness and existence of a class of weak solutions (the so called BV solutions) of the Cauchy-Dirichlet problem associated to the doubly nonlinear diffusion equation b(u)t - div (|∇u - k(b(u))e|p-2 (∇u - k(b(u))e)) + g(x,u) = f(t,x). This problem arises in the study of some turbulent regimes: flows of incompressible turbulent fluids through porous media, gases flowing in pipelines, etc....
Natural and artificially controlled connections among steady states of a climate model.
Mathematical analysis of the discharge of a laminar hot gas in a colder atmosphere.
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 proving the existence and uniqueness of solutions of the nondegenerate problem under assumptions implying that the temperature T and the horizontal velocity u of the gas are strictly positive: T ≥ δ > 0 and u ≥ ε > 0 (here δ and ε are given as boundary conditions in the external atmosphere)....
On the Newton partially flat minimal resistance body type problems
We study the flat region of stationary points of the functional under the constraint , where is a bounded domain in . Here is a function which is concave for small and convex for large, and 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 is a ball. We also analyze some other qualitative properties. Moreover, we show the...
Some results about multiplicity and bifurcation of stationary solutions of a reaction diffusion climatological model.
In this survey we collect several results concerning S-type bifurcation curves for the number of solutions of reaction-diffusion stationary equations. In particular, we recall several results in the literature for the case of stationary energy balance models.
Stopping a viscous fluid by a feedback dissipative field: II. The stationary Navier-Stokes problem
We consider a planar stationary flow of an incompressible viscous fluid in a semi-infinite strip governed by the Navier-Stokes system with a feed-back body forces field which depends on the velocity field. Since the presence of this type of non-linear terms is not standard in the fluid mechanics literature, we start by establishing some results about existence and uniqueness of weak solutions. Then, we prove how this fluid can be stopped at a finite distance of the semi-infinite strip entrance by...
A parabolic system involving a quadratic gradient term related to the Boussinesq approximation.
We propose a modification of the classical Boussinesq approximation for buoyancy-driven flows of viscous, incompressible fluids in situations where viscous heating cannot be neglected. This modification is motivated by unresolved issues regarding the global solvability of the original system. A very simple model problem leads to a coupled system of two parabolic equations with a source term involving the square of the gradient of one of the unknowns. Based on adequate notions of weak and strong...
The support shrinking properties for solutions of quasilinear parabolic equations with strong absorption terms
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