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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
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
We consider a 1-dimensional reaction–diffusion equation with nonlinear boundary conditions of logistic type with delay. We deal with non-negative solutions and analyze the stability behavior of its unique positive equilibrium solution, which is [...]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
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
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
We analyze the dynamics of a reaction–diffusion equation with homogeneous Neumann boundary conditions in a dumbbell domain. We provide an appropriate functional setting to treat this problem and, as a first step, we show in this paper the contin[...]texto impreso
Arrieta Algarra, José María ; Carvalho, Alexandre N. ; Lozada-Cruz, Germán | Academic Press | 2009-07-01In this work we continue the analysis of the asymptotic dynamics of reaction diffusion problems in a dumbbell domains started in [3]. Here we study the limiting problem, that is, an evolution problem in a \domain" which consists of an open, boun[...]texto impreso
In this work we continue the analysis of the asymptotic dynamics of reaction–diffusion problems in a dumbbell domain started in [J.M. Arrieta, A.N. Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J.[...]texto impreso
In this paper we conclude the analysis started in [3] and continued in [4] con- cerning the behavior of the asymptotic dynamics of a dissipative reactions di_usion equation in a dumbbell domain as the channel shrinks to a line segment. In [3], w[...]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
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[...]
