We construct exponential pullback attractors for time continuous asymptotically compact evolution processes in Banach spaces and derive estimates on the fractal dimension of the attractors. We also discuss the corresponding ...

This paper deals with the control problem of discrete-time Markov jump linear systems for the case in which the controller does not have access to the state of the Markov chain. A necessary optimal condition, which is ...

Given a Carnot-Carathéodory space Ω ⊆ ℝn with associated frame of vector fields X = {X<inf>1</inf>,⋯, X<inf>m</inf>}, we derive the subelliptic ∞-Laplace system for mappings u: Ω → ℝN, which reads δX∞u:=(Xu ⊗ Xu +

In this paper, we study the well-posedness in scales of Hilbert spaces Eα, α ∈ ℝ defined by the non-coupled system partial differential operator of a chemotaxis model of aggregation of microglia in Alzheimer's disease for ...

In this paper, we obtain the L∞-null controllability of the parabolic equation with equivalued surface boundary conditions in Ω×[0,T]. The control is supported in the product of an open subset of Ω and a subset of [0,T] ...

We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance ...

We consider degenerate parabolic equations of the form ∂tu = Δλu + f(u) u{pipe}∂Ω = 0, u{pipe}t=0 = u0 in a bounded domain Ω ⊂N, where Δλ is a subelliptic operator of the type (Formula presented.) We prove global existence ...

We study the positivity of solutions of a class of semi-linear parabolic systems of stochastic partial differential equations by considering random approximations. For the family of random approximations we derive explicit ...

We compare numerical experiments from the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method, applied to three benchmark problems based on two different ...

In this paper, a lower bound is established for the local energy of partial sum of eigenfunctions for Laplace-Beltrami operators (in Riemannian manifolds with low regularity data) with general boundary condition. This ...