Información del autor
Autor Carrillo Menéndez, José |
Documentos disponibles escritos por este autor (31)
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In a bounded domain Omega we study the existence and uniqueness of entropy solutions of partial derivativeu/partial derivativet + div Phi(u) = f with u(0) = u(0), where Phi is allowed to have some discontinuities of first type.![]()
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This conference contribution gives a brief introduction to the resolution of some degenerate problems with the L1 theory in open bounded sets. The first part of the work describes well known concepts related to entropy solutions of Kruzhkov and [...]![]()
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We consider a class of elliptic-hyperbolic degenerate equations g(u) - Delta b(u) + div phi (u) = f with Dirichlet homogeneous boundary conditions and a class of elliptic-parabolic-hyperbolic degenerate equations g(u)(t) - Delta b(u) + div phi ([...]![]()
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This article studies a filtration problems with nonlinear Darcy’s law, e.g. ~v = ?|rp|q?2rp, where p is the fluid pressure , q > 1, and ~v is the velocity, governed by the mass conservation law div(~v) = 0. This leads to a free boundary problem[...]![]()
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We consider a free boundary problem related to a stationary flow of fresh and salt water in a coastal aquifer. The flow is governed by a nonlinear Darcy’s law. Existence and uniqueness of a monotone solution are proved.![]()
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We study a problem related to the lubrication with cavitation arising in bearings. This problem was previously studied by {\it G. Bayada} and {\it M. Chambat} [Boll. Unione Mat. Ital., IV. Ser., B 3, 543-557 (1984)]. They stated the problem and [...]![]()
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The existence of weak solutions of the Dirichlet problem for nonlinear elliptic equations of the type ?(?/?x j )(a ij (x)u x i +b j (u))+a(x)u=f is proved for nonlinearities b j which are only continuous. The proof is based on the observatio[...]![]()
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This paper is concerned with the qualitative behavior of solutions of the "dam problem'' for flow of an incompressible fluid through a two-dimensional porous medium. The cross section of the flow region is allowed to have a complicated boundary [...]![]()
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The purpose here is to investigate some aspects of the evolution dam problem $\partial(\chi+\alpha u)/\partial t=\Delta u+{\rm div}(\chi e)$ in $Q$, $\chi\in H(u)$ in $Q$, $u\geq 0$ in $Q$, in $\Sigma_2$, $\partial u/\partial v+\chi ev\[...]![]()
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We study an initial boundary value problem for a scalar conservation law u(t) + div Phi(u) = f on a bounded domain. Existence and uniqueness of a renormalized entropy solution is established for general L-1-data, Phi is an element ofC(R, R-N![]()
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We introduce a notion of entropy solution for a scalar conservation law on a bounded domain with nonhomogeneous boundary condition: u(t) + div Phi (u) = f on Q = (0, T) x Omega, u (0, (.))= u(0) on Q and "u = a on some part of the boundary (0, T[...]![]()
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We consider a class of elliptic-hyperbolic degenerate equations g(u) - Delta b(u) + div phi(u) = f With Dirichlet homogeneous boundary conditions, and a class of elliptic-parabolic-hyperbolic degenerate equations g(u)(t) - Delta b(u) + div phi(u[...]![]()
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The subject of this paper is the study of a free boundary problem for a steady fluid flow through a porous medium, in which the classical Darcy law (1) ?!v = ar(p(x)+xn), x = (x1, · · · , xn) 2 Rn, a > 0, is replaced by the nonlinear law (2) |?[...]![]()
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The goal of this paper is to study the fluid flow through a two-dimensional porous medium when we impose a leaky boundary condition. We show in particular that the situation is quite different from the one with the usual Dirichlet boundary condition.![]()
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We study the support of the solution of the dam problem and estimate its growth from above and from below for small t . We derive sufficient conditions in order that it grows with finite or infinite speed. Moreover a monotonicity result for the [...]![]()
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We prove uniqueness and the L-1-comparison principle Sor renormalized solutions of the elliptic-parabolic problem associated with the equation b(upsilon)(t) = div a(upsilon, D upsilon) + f.![]()
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We prove uniqueness of the Krushov solution of the equation ?u+div((u))+ au 3 f 0 with homogeneous boundary datum. Is not necessarily continuous![]()
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We consider a general class of degenerate elliptic-paraboic problems associated with the equation b(v)(t) = div a(v, Dv) + f. Using Kruzhkov's method of doubling variables both in space and time we prove uniqueness and a comparison principle in [...]![]()
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In this paper we study the speed of propagation of the free boundary of the dam problem. We prove that the free boundary of the saturated part (X = 1) has a finite speed of propagation, which implies that the speed of propagation of the pressure[...]