Related papers: Singularly perturbed hyperbolic problems on metric…
We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and…
A semi-linear parabolic problem is considered in a thin $3D$ star-shaped junction that consists of several thin curvilinear cylinders that are joined through a domain (node) of diameter $\mathcal{O}(\varepsilon).$ The purpose is to study…
This paper investigates the initial boundary value problem of a finitely degenerate semilinear pseudo-parabolic equation associated with H\"{o}rmander's operator. Based on the global existence of solutions in previous literature, the…
Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are…
We study expansions near the boundary of solutions to the Dirichlet problem for the constant mean curvature equation in the hyperbolic space. With a characterization of remainders of the expansion by multiple integrals, we establish optimal…
Model two-dimensional singular perturbed eigenvalue problem for Laplacian with frequently alternating type of boundary condition is considered. Complete two-parametrical asymptotics for the eigenelements are constructed.
An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be written as a Laplacian growth model regularized by a `kinetic undercooling' boundary condition. We study the linear stability of uniformly…
In this work a discontinuous boundary-value problem with retarded argument which contains spectral parameter in the transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas for the eigenvalues…
The paper deals with initial-boundary value problems for linear non-autonomous first order hyperbolic systems whose solutions stabilize to zero in a finite time. We prove that problems in this class remain exponentially stable in $L^2$ as…
We study boundary value problems for degenerate elliptic equations and systems with square integrable boundary data. We can allow for degeneracies in the form of an $A_{2}$ weight. We obtain representations and boundary traces for solutions…
We study a class of degenerate parabolic equations with boundary point degeneracy in dimensions N>=2 and investigate the associated boundary observability problem by means of shape design. While one-dimensional degenerate models have been…
We consider a nonlinear singularly perturbed PDE leaning on a complex perturbation parameter $\epsilon$. The problem possesses an irregular singularity in time at the origin and involves a set of so-called moving turning points merging to 0…
Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set,…
This paper presents an approach to study initial-boundary value (IBV) problems for integrable nonlinear differential-difference equations (DDEs) posed on a graph. As an illustrative example, we consider the Ablowitz-Ladik system posed on a…
Hierarchical graphs often exhibit tree-like branching patterns, a structural property that challenges the design of traditional graph filters. We introduce a boundary-weighted operator that rescales each edge according to how far its…
It was shown recently that the constraints on the initial data for Einstein's equations may be posed as an evolutionary problem [9]. In one of the proposed two methods the constraints can be replaced by a first order symmetrizable…
We enumerate the connected graphs that contain a number of edges growing linearly with respect to the number of vertices. So far, only the first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, ie…
The initial boundary value problem for a Cahn-Hilliard system subject to a dynamic boundary condition of Allen-Cahn type is treated. The vanishing of the surface diffusion on the dynamic boundary condition is the point of emphasis. By the…
Motivated by an analysis on the well-posedness of the initial boundary value problem for the motion of an inextensible hanging string, we first consider an initial boundary value problem for one-dimensional degenerate hyperbolic systems…
This work is devoted to study of a class of elliptic singular perturbed systems and their singular limit to a phase segregating system. We prove existence and uniqueness and study the asymptotic behaviour with convergence to a limiting…