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This note is devoted to some nonlocal, nonlinear elliptic problems with an emphasis on the computation of the solution of such problems, reducing it in particular to a fixed point argument in R. Errors estimates and numerical experiments…

In this paper, we propose a mesh-free method to solve interface problems using the deep learning approach. Two interface problems are considered. The first one is an elliptic PDE with a discontinuous and high-contrast coefficient. While the…

We study a certain one dimensional, degenerate parabolic partial differential equation with a boundary condition which arises in pricing of Asian options. Due to degeneracy of the partial differential operator and the non-smooth boundary…

In this note, a novel observer-based output feedback control approach is proposed to address the distributed optimal output consensus problem of uncertain nonlinear multi-agent systems in the normal form over unbalanced directed graphs. The…

In this paper, we present a distributed algorithm for solving convex, constraint-coupled, optimization problems over peer-to-peer networks. We consider a network of processors that aim to cooperatively minimize the sum of local cost…

In this paper we perform the rigorous derivation of the topological derivative for optimization problems constrained by a class of quasi-linear elliptic transmission problems. In the case of quasi-linear constraints, techniques using…

We investigate an overdetermined Torsion problem, with a non-constant positively homogeneous boundary constraint on the gradient. We interpret this problem as the Euler equation of a shape optimization problems, we prove existence and…

In Bayesian peer-to-peer decentralized data fusion, the underlying distributions held locally by autonomous agents are frequently assumed to be over the same set of variables (homogeneous). This requires each agent to process and…

We consider the problem of global in time existence and uniqueness of solutions of the 3-D infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher…

In this paper, we introduce a class of high order immersed finite volume methods (IFVM) for one-dimensional interface problems. We show the optimal convergence of IFVM in H1 and L2 norms. We also prove some superconvergence results of IFVM.…

In this paper we consider nonlinear parabolic systems with elliptic part which can be also degenerate. We prove optimal error estimates for smooth enough solutions. The main novelty, with respect to previous results, is that we obtain the…

The paper continues the analysis, started in [1] (Part I,arXiv:2302.04353), of the model open wave-guide problem defined by 2 semi-infinite, rectangular wave-guides meeting along a common perpendicular line. In Part I we reduce the solution…

In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…

When a spatially localized stress is applied to a growing one-dimensional interface, the interface deforms. This deformation is described by the effective surface tension representing the stiffness of the interface. We present that the…

We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.

The large time behaviour of nonnegative solutions to a quasilinear degenerate diffusion equation with a source term depending solely on the gradient is investigated. After a suitable rescaling of time, convergence to a unique profile is…

We consider asymptotic problems concerning the motion of interface separating the regions of large and small values of the solution of a reaction-diffusion equation in the media consisting of domains with different characteristics…

A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…

An unbounded one-dimensional solid-on-solid model with integer heights is studied. Unbounded here means that there is no a priori restrictions on the discret e gradient of the interface. The interaction Hamiltonian of the interface is given…

We formulate a general shape and topology optimization problem in structural optimization by using a phase field approach. This problem is considered in view of well-posedness and we derive optimality conditions. We relate the diffuse…