Información del autor
Autor Rodríguez Bernal, Aníbal |
Documentos disponibles escritos por este autor (73)
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Arrieta Algarra, José María ; Cholewa, Jan W. ; Dlotko, Tomasz ; Rodríguez Bernal, Aníbal | Elsevier | 2004In this paper we give general and flexible conditions for a reaction diffusion equation to be dissipative in an-unbounded domain. The functional setting is based on standard Lebesgue and Sobolev-Lebesgue spaces. We show how the reaction and diff[...]texto impreso
Arrieta Algarra, José María ; Pardo San Gil, Rosa ; Rodríguez Bernal, Aníbal | Elsevier | 2015-12-05We analyze the asymptotic behavior of positive solutions of parabolic equations with a class of degenerate logistic nonlinearities of the type lambda u - n(x)u(rho). An important characteristic of this work is that the region where the logistic [...]texto impreso
In this paper we analyze the long time behavior of a phase field model by showing the existence of global compact attractors in the strong norm of high order Sobolev spaces.texto impreso
We analyze the asymptotic behavior of the attractors of a parabolic 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 epsilo[...]texto impreso
In this paper, we establish the global fast dynamics for the time-dependent Ginzburg-Landau equations of superconductivity. We show the squeezing property and the existence of finite-dimensional exponential attractors for the system. In addition[...]texto impreso
The title of the paper says it all. The author considers a reaction-diffusion equation with nonlinear boundary conditions on a bounded domain ??R N . The initial value u 0 is allowed to be a function in L r (?) , with 1texto impreso
In this paper, we study the asymptotic behavior of solutions for the partly dissipative reaction diffusion equations in R-n. We prove the asymptotic compactness of the solutions and then establish the existence of the global attractor in L-2(R-n[...]texto impreso
Arrieta Algarra, José María ; Carvalho, Alexandre N. ; Rodríguez Bernal, Aníbal | Taylor & Francis | 2000The authors study the asymptotic behavior of solutions to a semilinear parabolic problem u t ?div(a(x)?u)+c(x)u=f(x,u) for u=u(x,t), t> 0, x????R N , a(x)> m> 0; u(x,0)=u 0 with nonlinear boundary conditions of the form u=0 on ? 0 , and a(x[...]texto impreso
Arrieta Algarra, José María ; Pardo San Gil, Rosa ; Rodríguez Bernal, Aníbal | Cambridge University Press | 2007-04We consider an elliptic equation with a nonlinear boundary condition which is asymptotically linear at infinity and which depends on a parameter. As the parameter crosses some critical values, there appear certain resonances in the equation prod[...]texto impreso
Arrieta Algarra, José María ; Rodríguez Bernal, Aníbal ; Souplet, Philippe | Scuola Normale Superiore | 2004We consider a one-dimensional semilinear parabolic equation with a gradient nonlinearity. We provide a complete classification of large time behavior of the classical solutions u: either the space derivative u., blows up in finite time (with u i[...]texto impreso
The Cauchy problem for the time-dependent Ginzburg-Landau equations of superconductivity in R-d (d = 2, 3) is investigated in this paper. When d = 2, we show that the Cauchy problem for this model is well posed in L-2. When d = 3, we establish t[...]texto impreso
We study the possible continuation of solutions of a nonlinear parabolic problem after the blow-up time. The nonlinearity in the equation is dissipative and blow-up is caused by the nonlinear boundary condition of the form ?u/??=|u|q-1u, where q[...]texto impreso
The dynamics of a closed thermosyphon are considered. Using an explicit construction, obtained through an inertial manifold, exact low-dimensional models are derived. The behavior of solutions is analyzed for different ranges of the relevant par[...]texto impreso
Arrieta Algarra, José María ; Carvalho, Alexandre N. ; Langa, José A. ; Rodríguez Bernal, Aníbal | Springer | 2012-09In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous d[...]texto impreso
Due to the lack of the maximum principle the analysis of higher order parabolic problems in RN is still not as complete as the one of the second-order reaction-diffusion equations. While the critical exponents and then a dissipative mechanism in[...]texto impreso
Arrieta Algarra, José María ; Carvalho, Alexandre N. ; Rodríguez Bernal, Aníbal | Elsevier | 1998-08We prove existence, uniqueness and regularity of solutions for heat equations with nonlinear boundary conditions. We study these problems with initial data in L-q(Ohm), W-1,W-q(Ohm), 1texto impreso
Rodríguez Bernal, Aníbal ; Van Vleck, Erik S. | Society for Industrial and Applied Mathematics | 1998-08The dynamics of a closed loop thermosyphon are considered. The model assumes a prescribed heat flux along the loop wall and the contribution of axial diffusion. The well-posedness of the model which consists of a coupled ODE and PDE is shown for[...]texto impreso
It is known that the concept of dissipativeness is fundamental for understanding the asymptotic behavior of solutions to evolutionary problems. In this paper we investigate the dissipative mechanism for some semilinear fourth-order parabolic equ[...]texto impreso
Arrieta Algarra, José María ; Cholewa, Jan W. ; Dlotko, Tomasz ; Rodríguez Bernal, Aníbal | Wiley-Blackwell | 2007The Cauchy problem for a semilinear second order parabolic equation u(t) = Delta u + f (x, u, del u), (t, x) epsilon R+ x R-N, is considered within the semigroup approach in locally uniform spaces W-U(s,p) (R-N). Global solvability, dissipativen[...]texto impreso
Jiménez Casas, Ángela ; Rodríguez Bernal, Aníbal | American Institute of Mathematical Sciences | 2011We obtain dynamic boundary conditions as a limit of parabolic problems with null flux where the time derivative concentrates near the boundary.texto impreso
We obtain nonhomogeneous dynamic boundary conditions as a singular limit of a parabolic problem with null flux and potentials and reaction terms concentrating at the boundary.texto impreso
Arrieta Algarra, José María ; Rodríguez Bernal, Aníbal ; Valero , José | World Scientific Publishing | 2006We study the nonlinear dynamics of a reaction-diffusion equation where the nonlinearity presents a discontinuity. We prove the upper semicontinuity of solutions and the global attractor with respect to smooth approximations of the nonlinear term[...]texto impreso
In this Note we study the asymptotic behavior of reaction diffusion equations with nonlinear boundary conditions. We obtain balance conditions between the reaction term and the nonlinear flux term which imply boundedness of solutions or blow-up [...]texto impreso
Arrieta Algarra, José María ; Pardo San Gil, Rosa María ; Rodríguez Bernal, Aníbal | Elsevier | 2009We consider a parabolic equation ut??u+u=0 with nonlinear boundary conditions , where as |s|??. In [J.M. Arrieta, R. Pardo, A. Rodríguez-Bernal, Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity[...]texto impreso
Rodríguez Bernal, Aníbal ; Vidal López, Alejandro ; Langa, J.A. ; Robinson, James C. ; Suárez, A. | American Institute of Mathematical Sciences | 2007The goal of this work is to study the forward dynamics of positive solutions for the nonautonomous logistic equation ut ? _u = _u ? b(t)up, with p > 1, b(t) > 0, for all t 2 R, limt!1 b(t) = 0. While the pullback asymptotic behaviour for this [...]