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Autor Rodríguez Bernal, Aníbal |
Documentos disponibles escritos por este autor (73)
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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 [...]texto impreso
Rodríguez Bernal, Aníbal ; Vidal López, Alejandro | American Institute of Mathematical Sciences | 2007We give conditions for the existence of a unique positive complete trajectories for non-autonomous reaction-diffusion equations. Also, attraction properties of the unique complete trajectory is obtained in a pullback sense and also forward in ti[...]texto impreso
The authors find a growth condition on the nonlinear term f(x, u) of a nonlinear heat equation which ensures the existence of maximal and minimal equilibria that bound asymptotically all solutions to that nonlinear heat equation.texto impreso
We consider a reaction diffusion equation u(t) = Delta u + f(x, u) in R-N with initial data in the locally uniform space (L) over dot(U)(q)(R-N), q is an element of [1, infinity), and with dissipative nonlinearities satisfying sf(x, s) N/2. U[...]texto impreso
In this well-written paper, the authors consider monotone semigroups in ordered spaces and give general results concerning the existence of extremal equilibria and global attractors. \par In the first part of the paper, some notions concerning d[...]texto impreso
We show the existence of two special equilibria, the extremal ones, for a wide class of reaction–diffusion equations in bounded domains with several boundary conditions, including non-linear ones. They give bounds for the asymptotic dynamics and[...]