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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
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
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
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
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
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
Cholewa, Jan W. ; Rodríguez Bernal, Aníbal | Institute of Mathematics, Academy of Sciences of the Czech Republic | 2014We consider the Cahn-Hilliard equation in H1(RN ) with two types of critically growing nonlinearities: nonlinearities satisfying a certain limit condition as |u| ? ? and logistic type nonlinearities. In both situations we prove the H2(RN )-bound[...]
