Related papers: On some 1D nonlocal models with coefficients chang…
We prove a global existence result for weak solutions to a one-dimensional free boundary problem with flux boundary conditions describing swelling along a halfline. Additionally, we show that solutions are not only unique but also depend…
Nonlocal models provide accurate representations of physical phenomena ranging from fracture mechanics to complex subsurface flows, where traditional partial differential equations fail to capture effects caused by long-range forces at the…
This paper investigates an elliptic interface problem with discontinuous diffusion coefficients on unfitted meshes, employing the CutFEM method. The main contribution is the a posteriori error analysis based on equilibrated fluxes belonging…
This article is devoted to the study of certain models for phase transitions involving nonlocal energies. A first part is concerned with to the asymptotic analysis of a system of fractional elliptic equations of Allen-Cahn type as a…
In this article we compare solutions to elliptic problems having rapidly oscillated conductivity (permeability, etc) coefficient with solutions to corresponding homogenized problems obtained from two-scale extensions of the initial…
In this paper we study a nonlocal critical growth elliptic problem driven by the fractional Laplacian in presence of jumping nonlinearities. In the main results of the paper we prove the existence of a nontrivial solution for the problem…
Using the T-coercivity theory as advocated in [Chesnel, Ciarlet, T -coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients (2013)], we propose a new variational formulation of the…
This article is concerned with the derivation of numerical reconstruction schemes for the inverse moving source problem on determining source profiles in (time-fractional) evolution equations. As a continuation of the theoretical result on…
This paper studies the estimation of linear panel data models with interactive fixed effects, where one dimension of the panel, typically time, may be fixed. To this end, a novel transformation is introduced that reduces the model to a…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
In this paper, a shape optimization problem constrained by a random elliptic partial differential equation with a pure Neumann boundary is presented. The model is motivated by applications in interface identification, where we assume…
Models of physical phenomena that use nonlocal operators are better suited for some applications than their classical counterparts that employ partial differential operators. However, the numerical solution of these nonlocal problems can be…
We propose a simple, exactly solvable, model of interface growth in a random medium that is a variant of the zero-temperature random-field Ising model on the Cayley tree. This model is shown to have a phase diagram (critical depinning field…
In this paper we investigate a class of elliptic problems involving a nonlocal Kirchhoff type operator with variable coefficients and data changing its sign. Under appropriated conditions on the coefficients, we have shown existence and…
We introduce a new kinetic interface model suitable for simulating adsorption-reaction processes which take place preferentially at surface defects such as steps and vacancies. As the average interface velocity is taken to zero, the self-…
We consider a scalar diffusion equation with a sign-changing coefficient in its principle part. The well-posedness of such problems has already been studied extensively provided that the contrast of the coefficient is non-critical.…
In this paper, new unfitted mixed finite elements are presented for elliptic interface problems with jump coefficients. Our model is based on a fictitious domain formulation with distributed Lagrange multiplier. The relevance of our…
Based on the development in dealing with nonlocal boundary conditions, we propose a seamless local-nonlocal coupling diffusion model in this paper. In our model, a finite constant interaction horizon is equipped in the nonlocal part and…
In multi-phase fluid flow, fluid-structure interaction, and other applications, partial differential equations (PDEs) often arise with discontinuous coefficients and singular sources (e.g., Dirac delta functions). These complexities arise…
Interfaces advancing through random media represent a number of different problems in physics, biology and other disciplines. Here, we study the pinning/depinning transition of the prototypical non-equilibrium interfacial model, i.e. the…