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Autor Rodríguez Bernal, Aníbal |
Documentos disponibles escritos por este autor (73)
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We analyse the dynamics of a fluid transporting a soluble substance in the interior of a closed loop of arbitrary geometry and subjected to the action of gravity and natural convection. After obtaining the governing equations and analysing the w[...]texto impreso
Arrieta Algarra, José María ; Jiménez Casas, Ángela ; Rodríguez Bernal, Aníbal | World Scientific Publ Co Pte Ltd | 2005We analyze the limit of solutions of an elliptic problem, with zero flux boundary conditions when the reaction terms are concentrated in a neighborhood of the boundary and that shrinks to the boundary as a parameter goes to zero. We prove that t[...]texto impreso
Arrieta Algarra, José María ; Jiménez Casas, Ángela ; Rodríguez Bernal, Aníbal | Universidad Autónoma Madrid | 2008We analyze the limit of the solutions of an elliptic problem when some reaction and potential terms are concentrated in a neighborhood of a portion Gamma of the boundary and this neighborhood shrinks to Gamma as a parameter goes to zero. We prov[...]texto impreso
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Arrieta Algarra, José María ; Pardo San Gil, Rosa María ; Rodríguez Bernal, Aníbal | World Scientific Publishing | 2010Summary: "We consider an elliptic equation ??u+u=0 with nonlinear boundary conditions ?u/?n=?u+g(?,x,u) , where (g(?,x,s))/s?0 as |s|?? . In [Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), no. 2, 225--252; MR2360769 (2009d:35194); J. Differentia[...]texto impreso
In this paper we consider some fourth order linear and semilinear equations in R-N and make a detailed study of the solvability of the Cauchy problem. For the linear equation we consider some weakly integrable potential terms, and for any 1texto impreso
Linear 2m-th order uniformly elliptic operators are shown to generate semigroups of bounded linear operators with suitable smoothing properties in scales of locally uniform Bessel's and Lebesgue's spaces.texto impreso
The aim of this paper is to provide a comprehensive study of some linear non-local diffusion problems in metric measure spaces. These include, for example, open subsets in ?N, graphs, manifolds, multi-structures and some fractal sets. For this, [...]texto impreso
Arrieta Algarra, José María ; Rodríguez Bernal, Aníbal ; Cholewa, Jan W. ; Dlotko, Tomasz | World Scientific | 2004We analyze the linear theory of parabolic equations in uniform spaces. We obtain sharp L-p - L-q-type estimates in uniform spaces for heat and Schrodinger semigroups and analyze the regularizing effect and the exponential type of these semigroup[...]texto impreso
We study the linear stability of equilibrium points of a semilinear phase-field model, giving criteria for stability and instability. In the one-dimensional case, we study the distribution of equilibria and also prove the existence of metastable[...]texto impreso
In this work we analyze the existence of solutions that blow-up in finite time for a reaction-diffusion equation ut??u=f(x,u) in a smooth domain ? with nonlinear boundary conditions ?u?n=g(x,u). We show that, if locally around some point of the [...]texto impreso
Arrieta Algarra, José M. ; Pardo, Rosa ; Rodríguez Bernal, Aníbal | Department of Mathematics Texas State University | 2014We analyze the behavior of positive solutions of elliptic equations with a degenerate logistic nonlinearity and Dirichlet boundary conditions. Our results concern existence and strong localization in the spatial region in which the logistic nonl[...]texto impreso
We analyze singular perturbations in elliptic equations, subjected to various boundary conditions, in which the diffusion is going to infinity in localized regions inside the domain and therefore solutions undergo a localized spatial homogenizat[...]texto impreso
We study the asymptotic behaviour in large diffusivity of inertial manifolds governing the long time dynamics of a semilinear evolution system of reaction and diffusion equations. A priori, we review both local and global dynamics of the system [...]texto impreso
Arrieta Algarra, José María ; Rodríguez Bernal, Aníbal | World Scientific Publ. Co. Pte. Ltd. | 2004-10In this paper we show that several known critical exponents for nonlinear parabolic problems axe optimal in the sense that supercritical problems are ill posed in a strong sense. We also give an answer to an open problem proposed by Brezis and C[...]