Related papers: Weak topologies for Carath\'{e}odory differential …
We study some already introduced and some new strong and weak topologies of integral type to provide continuous dependence on continuous initial data for the solutions of non-autonomous Carath\'eodory delay differential equations. As a…
The first part of the paper is devoted to studying the continuous dependence of the solutions of Carath\'eodory constant delay differential equations where the vector fields satisfy classical cooperative conditions. As a consequence, when…
Metric topological vector spaces of Carath\'eodory functions and topologies of $L^p_{loc}$ type are introduced, depending on a suitable set of moduli of continuity. Theorems of continuous dependence on initial data for the solutions of…
Considering evolutionary equations in the sense of Picard, we identify a certain topology for material laws rendering the solution operator continuous if considered as a mapping from the material laws into the set of bounded linear…
Two one-parametric bifurcation problems for scalar nonautonomous ordinary differential equations are analyzed assuming the coercivity of the time-dependent function determining the equation and the concavity of its derivative with respect…
In this paper a family of non-autonomous scalar parabolic PDEs over a general compact and connected flow is considered. The existence or not of a neighbourhood of zero where the problems are linear has an influence on the methods used and…
The propagation of internal gravity waves in stratified media, such as those found in ocean basins and lakes, leads to the development of geometrical patterns called "attractors". These structures accumulate much of the wave energy and make…
We consider two-dimensional nonstationary Navier-Stokes shear flow with multivalued and nonmonotone boundary conditions on a part of the boundary of the flow domain. We prove the existence of global in time solutions of the considered…
We establish the well-posedness of a strongly damped semilinear wave equation equipped with nonlinear hyperbolic dynamic boundary conditions. Results are carried out with the presence of a parameter distinguishing whether the underlying…
Systems of non-autonomous parabolic partial differential equations over a bounded domain with nonlinear term of Carath\'eodory type are considered. Appropriate topologies on sets of Lipschitz Carath\'eodory maps are defined in order to have…
In this paper, we consider the asymptotic behavior of weak solutions for non-autonomous diffusion equations with delay in time-dependent spaces when the nonlinear function $f$ is critical growth, the delay term $g(t, u_t)$ contains some…
An abstract framework for studying the asymptotic behavior of a dissipative evolutionary system $\mathcal{E}$ with respect to weak and strong topologies was introduced in [8] primarily to study the long-time behavior of the 3D Navier-Stokes…
In this paper, we consider global weak solutions to com-pressible Navier-Stokes-Korteweg equations with density dependent viscosities , in a periodic domain $\Omega = \mathbb T^3$, with a linear drag term with respect to the velocity. The…
We give explicit solutions to the two-component Hunter-Saxton system on the unit circle. Moreover, we show how global weak solutions can be naturally constructed using the geometric interpretation of this system as a re-expression of the…
Results on continuous dependence on parameters, as well as on regularization, of solutions to linear systems of parabolic partial differential equations of second order with delay are given. One of the main features is that the topology on…
In this paper, we consider the asymptotic behavior of weak solutions for nonclassical non-autonomous diffusion equations with a delay operator in time-dependent spaces when the nonlinear function $g$ satisfies subcritical exponent growth…
As it is well-known, the forwards and pullback dynamics are in general unrelated. In this paper we present an in-depth study of whether the pullback attractor is also a forwards attractor for the processes involved with the skew-product…
The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…
In view of the possibility that the 3D Navier-Stokes equations (NSE) might not always have regular solutions, we introduce an abstract framework for studying the asymptotic behavior of multi-valued dissipative evolutionary systems with…
In this paper we obtain a detailed description of the global and cocycle attractors for the skew-product semiflows induced by the mild solutions of a family of scalar linear-dissipative parabolic problems over a minimal and uniquely ergodic…