Related papers: Nonlocal and mixed models with Lavrentiev Gap
The large-time asymptotics of the solutions to a class of degenerate parabolic cross-diffusion systems is analyzed. The equations model the interaction of an arbitrary number of population species in a bounded domain with no-flux boundary…
This work is devoted to the study of the existence of solutions to nonlocal equations involving the fractional Laplacian. These equations have a variational structure and we find a nontrivial solution for them using the Mountain Pass…
We consider a diffuse interface model for an incompressible isothermal mixture of two viscous Newtonian fluids with different densities in a bounded domain in two or three space dimensions. The model is the nonlocal version of the one…
Local-to-Nonlocal (LtN) coupling refers to a class of methods aimed at combining nonlocal and local modeling descriptions of a given system into a unified coupled representation. This allows to consolidate the accuracy of nonlocal models…
We prove global-local mixing for a large class of dynamical systems with infinite invariant measure. In particular, we treat intermittent maps including maps with multiple neutral fixed points, nonMarkovian intermittent maps, and…
In this paper, we consider a family of seamlessly coupled nonlocal models associated with transmission conditions across an interface. The models are derived from the variation of a parameterized family of energies consisting of a…
We study Neumann type boundary value problems for nonlocal equations related to L\'evy processes. Since these equations are nonlocal, Neumann type problems can be obtained in many ways, depending on the kind of reflection we impose on the…
In the present article we investigate a boundary problem with non-local conditions for mixed parabolic-hyperbolic type equation with three lines of type changing. Considered mixed domain contains a rectangle as a parabolic part and three…
In this thesis we investigate how the nonlocalities affect the study of different PDEs coming from physics, and we analyze these equations under almost optimal assumptions of the nonlinearity. In particular, we focus on the fractional…
Recently, it was claimed that the two-phase local/nonlocal constitutive models give well-posed nonlocal field problems and eliminates the ill-posedness of the fully nonlocal constitutive models. In this study, it is demonstrated that, both,…
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…
We discuss a Lipschitz truncation technique for parabolic double-phase problems of $p$-Laplace type in order to prove energy estimates and uniqueness results for the Dirichlet problem. Moreover, we show existence for a non-homogeneous…
We study a nonlocal version of the two-phase Stefan problem, which models a phase transition problem between two distinct phases evolving to distinct heat equations. Mathematically speaking, this consists in deriving a theory for…
Phase-field models are a popular choice in computational physics to describe complex dynamics of substances with multiple phases and are widely used in various applications. We present nonlocal non-isothermal phase-field models of…
In this article the correctness of al inear inverse problem with semi-nonlocal boundary conditions for a three-dimensional equation in a parallelepiped is considered. The equation itself is a fourth order mixed type equation of the second…
Many Polyakov loop models can be written in a dual formulation which is free of sign problem even when a non-vanishing baryon chemical potential is introduced in the action. Here, results of numerical simulations of a dual representation of…
In this paper we extend some results presented in \cite{julio} to the case of the $p$-Laplacian operator. More precisely, we consider a model that couples a local $p$-Laplacian operator with a nonlocal $p$-Laplacian operator through source…
This paper presents the first asynchronous version of the Global/Local non-invasive coupling, capable of dealing efficiently with multiple, possibly adjacent, patches. We give a new interpretation of the coupling in terms of primal domain…
This survey offers an overview of recent advances in nonlocal phase transition problems, modeled by Ginzburg--Landau type energies of the form \[ \frac{1}{4}\iint_{\R^{2n}\setminus (\R^n \setminus \Omega)^2}…
Two-place nonlocal systems have attracted many scientists' attentions. In this paper, two-place non-localities are extended to multi-place non-localities. Especially, various two-place and four-place nonlocal nonlinear Schrodinger (NLS)…