1,721,040 research outputs found
On the regularity of global attractors
No full textThis note is focused on a novel technique to establish the bound-
edness in more regular spaces for global attractors of dissipative dynamical systems, without appealing to uniform-in-time estimates. As an application,
we consider the semigroup generated by the strongly damped wave equation with critical nonlinearity, whose attractor is shown to possess the optimal regularity
Existence of ground states and free boundary problems for the prescribed mean curvature equation.
No full text
On the time-dependent Cattaneo law in space dimension one
Full text linkWe consider a one-dimensional wave equation with time-dependent coefficients which is proposed as a model for heat
conduction of Cattaneo type with thermal resistance decreasing in time. Within the theory
of processes on time-dependent spaces, we prove the existence of an invariant time-dependent
attractor, which converges in a suitable sense to the attractor of the classical
Fourier equationformally arising in the limit as time goes to infinity
Minimal coexistence configurations for multispecies systems
No full textWe deal with strongly competing multispecies systems of Lotka-Volterra type with
homogeneous Neumann boundary conditions in dumbbell-like domains. Under suitable
non-degeneracy assumptions, we show that, as the competition rate grows indefinitely, the
system reaches a state of coexistence of all the species in spatial segregation. Furthermore,
the limit configuration is a local minimizer for the associated free energy
A Remark on Nonclassical Diffusion Equations with Memory
Full text linkThe nonclassical diffusion equation with hereditary memory (Formula presented.) a 3D bounded domain is considered, for a very general class of memory kernels (Formula presented.). Setting the problem both in the classical past history framework and in the more recent minimal state one, the related solution semigroups are shown to possess finite-dimensional regular exponential attractors
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