497 research outputs found
Global minimizers of coexistence for competing species
A class of variational models describing ecological systems of k species
competing for the same resources is investigated. The occurrence of coexistence
in minimal energy solutions is discussed and positive results are proven for
suitably differentiated internal dynamics
Coexistence and Segregation for Strongly Competing Species in Special Domains
We deal with strongly competing multispecies systems of Lotka-Volterra type
with homogeneous Dirichlet boundary conditions. For a class of nonconvex
domains composed by balls connected with thin corridors, we show the occurrence
of pattern formation (coexistence and spatial segregation of all the species),
as the competition grows indefinitely. As a result we prove the existence and
uniqueness of solutions for a remarkable system of differential inequalities
involved in segregation phenomena and optimal partition problems
Timoshenko systems with fading memory
The decay properties of the semigroup generated by a linear Timoshenko system
with fading memory are discussed. Uniform stability is shown to occur within a
necessary and sufficient condition on the memory kernel
Attractors for processes on time-dependent spaces. Applications to wave equations
For a process U(t,s) acting on a one-parameter family of normed spaces, we
present a notion of time-dependent attractor based only on the minimality with
respect to the pullback attraction property. Such an attractor is shown to be
invariant whenever the process is T-closed for some T>0, a much weaker property
than continuity (defined in the text). As a byproduct, we generalize the recent
theory of attractors in time-dependent spaces developed in [10]. Finally, we
exploit the new framework to study the longterm behavior of wave equations with
time-dependent speed of propagation
On the Cahn-Hilliard-Brinkman system
We consider a diffuse interface model for phase separation of an isothermal
incompressible binary fluid in a Brinkman porous medium. The coupled system
consists of a convective Cahn-Hilliard equation for the phase field ,
i.e., the difference of the (relative) concentrations of the two phases,
coupled with a modified Darcy equation proposed by H.C. Brinkman in 1947 for
the fluid velocity . This equation incorporates a diffuse interface
surface force proportional to , where is the so-called
chemical potential. We analyze the well-posedness of the resulting
Cahn-Hilliard-Brinkman (CHB) system for . Then we establish
the existence of a global attractor and the convergence of a given (weak)
solution to a single equilibrium via {\L}ojasiewicz-Simon inequality.
Furthermore, we study the behavior of the solutions as the viscosity goes to
zero, that is, when the CHB system approaches the Cahn-Hilliard-Hele-Shaw
(CHHS) system. We first prove the existence of a weak solution to the CHHS
system as limit of CHB solutions. Then, in dimension two, we estimate the
difference of the solutions to CHB and CHHS systems in terms of the viscosity
constant appearing in CHB
Averaging of equations of viscoelasticity with singularly oscillating external forces
Given , we consider for the nonautonomous
viscoelastic equation with a singularly oscillating external force together with the
{\it averaged} equation Under suitable assumptions on
the nonlinearity and on the external force, the related solution processes
acting on the natural weak energy space
are shown to possess uniform attractors . Within the
further assumption , the family turns out to
be bounded in , uniformly with respect to .
The convergence of the attractors to the attractor
of the averaged equation as is also
established
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