相关论文: Existence Theory for the EED Inpainting Problem

We consider the transmission eigenvalue problem for an impenetrable obstacle with Dirichlet boundary condition surrounded by a thin layer of non-absorbing inhomogeneous material. We derive a rigorous asymptotic expansion for the first…

The analytical method of solving the boundary problems for a system of equations describing the behaviour of electrons and an electric field in the Maxwell plasma half-space is developed. Here the diffusion reflection of electrons from the…

For a class of Bellman equations in bounded domains we prove that sub- and supersolutions whose growth at the boundary is suitably controlled must be constant. The ellipticity of the operator is assumed to degenerate at the boundary and a…

Trendy suggestions for learning-based elastic warps enable the deep image stitchings to align images exposed to large parallax errors. Despite the remarkable alignments, the methods struggle with occasional holes or discontinuity between…

An initial-boundary value problem for a time-fractional subdiffusion equation with an arbitrary order elliptic differential operator is considered. Uniqueness and existence of the classical solution of the posed problem are proved by the…

The theory of degenerate parabolic equations of the forms \[ u_t=(\Phi(u_x))_{x} \quad {\rm and} \quad v_{t}=(\Phi(v))_{xx} \] is used to analyze the process of contour enhancement in image processing, based on the evolution model of…

Image inpainting involves filling in damaged or missing regions of an image by utilizing information from the surrounding areas. In this paper, we investigate a highly nonlinear partial differential equation inspired by the modified…

Reconstruction-based approaches have achieved remarkable outcomes in anomaly detection. The exceptional image reconstruction capabilities of recently popular diffusion models have sparked research efforts to utilize them for enhanced…

The Blackstock-Crighton equation models nonlinear acoustic wave propagation in thermo-viscous fluids. In the present work we investigate the associated inhomogeneous Dirichlet and Neumann boundary value problems in a bounded domain and…

A monotone iterative method is proposed to solve nonlinear discrete boundary value problems with the support of upper and lower solutions. We establish some new existence results. Under some sufficient conditions, we establish maximum…

This paper investigates a reaction-advection-diffusion system modeling interspecific competition between two species over bounded domains. The kinetic terms are assumed to satisfy the Beddington-DeAngelis functional responses. We consider…

In this paper, we consider the existence and uniqueness of weak solutions of a nonlinear elliptic equation with a variable exponent, a monotonic type operator and a convection term. With the topological degree theory, we prove the existence…

We investigate an initial-(periodic-)boundary value problem for a continuum equation, which is a model for motion of grain boundaries based on the underlying microscopic mechanisms of line defects (disconnections) and integrated the effects…

In this paper a fourth order equation involving critical growth is considered under Navier boundary condition. We give some topological conditions on a given function to ensure the existence of solutions. Our methods involve the study of…

We prove existence and uniqueness of travelling waves for a reaction-diffusion system coupling a classical reaction-diffusion equation in a strip with a diffusion equation on a line. To do this we use a continuation method which leads to…

In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…

This paper is concerned with traveling waves to an diffusive SIR model with delay placed in the diffusion terms as well as nonlinear incidence rate with delay. Using a cross iteration scheme and partial monotone conditions it will be shown…

As artificial intelligence advances rapidly, particularly with the advent of GANs and diffusion models, the accuracy of Image Inpainting Localization (IIL) has become increasingly challenging. Current IIL methods face two main challenges: a…

We present here a review of existing analytical methods to solve boundary value problems of diffusion in media containing N non-overlapping inclusions.

In this paper we consider a coupled system of pdes modelling the interaction between a two--dimensional incompressible viscous fluid and a one--dimensional elastic beam located on the upper part of the fluid domain boundary. We design a…