301 research outputs found
On improvement of summability properties in nonautonomous Kolmogorov equations
Under suitable conditions, we obtain some characterization of
supercontractivity, ultraboundedness and ultracontractivity of the evolution
operator associated to a class of nonautonomous second order parabolic
equations with unbounded coefficients defined in , where is a
right-halfline. For this purpose, we establish an Harnack type estimate for
and a family of logarithmic Sobolev inequalities with respect to the
unique tight evolution system of measures associated to
. Sufficient conditions for the supercontractivity, ultraboundedness
and ultracontractivity to hold are also provided
Non autonomous parabolic problems with unbounded coefficients in unbounded domains
Given a class of nonautonomous elliptic operators \A(t) with unbounded
coefficients, defined in \overline{I \times \Om} (where is a
right-halfline or and \Om\subset \Rd is possibly unbounded), we prove
existence and uniqueness of the evolution operator associated to \A(t) in the
space of bounded and continuous functions, under Dirichlet and first order, non
tangential homogeneous boundary conditions. Some qualitative properties of the
solutions, the compactness of the evolution operator and some uniform gradient
estimates are then proved
-estimates for parabolic systems with unbounded coefficients coupled at zero and first order
We consider a class of nonautonomous parabolic first-order coupled systems in
the Lebesgue space , with . Sufficient conditions for the associated evolution operator in to extend to a strongly
continuous operator in are given. Some
- estimates are also established together with gradient
estimates
Invariant measures for systems of Kolmogorov equations
In this paper we provide sufficient conditions which guarantee the existence
of a system of invariant measures for semigroups associated to systems of
parabolic differential equations with unbounded coefficients. We prove that
these measures are absolutely continuous with respect to the Lebesgue measure
and study some of their main properties. Finally, we show that they
characterize the asymptotic behaviour of the semigroup at infinity
Strong convergence of solutions to nonautonomous Kolmogorov equations
We study a class of nonautonomous, linear, parabolic equations with unbounded
coefficients on which admit an evolution system of measures. It
is shown that the solutions of these equations converge to constant functions
as . We further establish the uniqueness of the tight evolution
system of measures and treat the case of converging coefficients
Two-dimensional stability analysis in a HIV model with quadratic logistic growth term
We consider a Human Immunodeficiency Virus (HIV) model with a logistic growth
term and continue the analysis of the previous article [6]. We now take the
viral diffusion in a two-dimensional environment. The model consists of two
ODEs for the concentrations of the target T cells, the infected cells, and a
parabolic PDE for the virus particles. We study the stability of the uninfected
and infected equilibria, the occurrence of Hopf bifurcation and the stability
of the periodic solutions.Comment: To appear on Commun. Pure Appl. Ana
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