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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[...]
