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In this paper, we propose to analyze stable and unstable modes of generic image denoisers through nonlinear eigenvalue analysis. We attempt to find input images for which the output of a black-box denoiser is proportional to the input. We…

Numerical Analysis · Mathematics 2020-07-07 Ester Hait-Fraenkel , Guy Gilboa

In this paper we consider a nonlinear Petrovsky equation in a bounded domain with a delay term and a strong dissipation \begin{align*} u_{tt} + \Delta^{2} u -\mu_1g_1( \Delta( u_t(x,t))) -\mu_2g_2( \Delta (u_t(x,t-\tau))) =0. \end{align*}…

Analysis of PDEs · Mathematics 2021-08-20 Ahmed Chahtou , Mama Abdelli , Akram Ben Aissa

This paper is addressed to the well-posedness of some linear and semilinear backward stochastic differential equations with general filtration, without using the Martingale Representation Theorem. The point of our approach is to introduce a…

Probability · Mathematics 2011-04-05 Qi Lu , Xu Zhang

We investigate a linear diffusion equation incorporating historical effects, characterised by a finite non-negative Borel measure on \((0, \mathfrak T]\). This approach accommodates both distributed memory and discrete delays within a…

Analysis of PDEs · Mathematics 2026-04-23 Hiroki Ishizaka

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…

Analysis of PDEs · Mathematics 2026-01-28 M. M. Chipot , A. Luthra , S. A. Sauter

We investigate local regularity properties of weak solutions to a broad class of nonlinear nonlocal kinetic Kolmogorov-Fokker-Planck equations. In particular, we focus on proving an interpolative apriori boundedness estimate for weak…

Analysis of PDEs · Mathematics 2025-08-29 Francesca Anceschi , Mirco Piccinini

We consider the classical Yang-Mills system coupled with a Dirac equation in 3+1 dimensions. Using that most of the nonlinear terms fulfill a null condition we prove local well-posedness for data with minimal regularity assumptions. This…

Analysis of PDEs · Mathematics 2021-12-08 Hartmut Pecher

We postulate a new nonlinear generalization of the Dirac equation for an electron. Basic properties of the new equation are considered.

Mathematical Physics · Physics 2019-10-21 Nikolay Marchuk

Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…

Information Theory · Computer Science 2017-01-11 Mohamed Suliman , Tarig Ballal , Tareq Y. Al-Naffouri

This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A…

Numerical Analysis · Mathematics 2020-08-26 Santiago Badia , Jesús Bonilla , Sibusiso Mabuza , John N. Shadid

In this work, we study the Dirichlet problem associated with a strongly coupled system of nonlocal equations. The system of equations comes from a linearization of a model of peridynamics, a nonlocal model of elasticity. It is a nonlocal…

Analysis of PDEs · Mathematics 2018-05-24 Moritz Kassmann , Tadele Mengesha , James Scott

We establish the global well-posedness of the $D(A)-$valued strong solution to a nonlinear heat equation with constraints on a \textit{Poincar\'e domain} $\bO\subset \R^d$ whose boundary is of class $C^2$. Consider the following nonlinear…

Analysis of PDEs · Mathematics 2025-12-25 Ashish Bawalia , Zdzisław Brzeźniak , Manil T. Mohan , Piotr Rybka

In this paper we obtain the existence of a radial solution for some elliptic nonlocal problem with constraints. The problem arises from some reaction-diffusion equation modelling among others system of self-gravitating particles when one…

Analysis of PDEs · Mathematics 2011-01-11 Robert Stańczy

In this paper, a compressible viscous-dispersive Euler system in one space dimension in the context of quantum hydrodynamics is considered. The purpose of this study is twofold. First, it is shown that the system is locally well-posed. For…

Analysis of PDEs · Mathematics 2023-09-04 Ramón G. Plaza , Delyan Zhelyazov

We study the planar front solution for a class of reaction diffusion equations in multidimensional space in the case when the essential spectrum of the linearization in the direction of the front touches the imaginary axis. At the linear…

Analysis of PDEs · Mathematics 2017-12-11 Anna Ghazaryan , Yuri Latushkin , Xinyao Yang

For a nonlinear diffusion equation on graphs whose nonlinearity violates the Lipschitz condition, we prove short-time solution existence and characterize global well-posedness by establishing sufficient criteria for blow-up phenomena and…

Analysis of PDEs · Mathematics 2025-04-16 Mengqiu Shao , Yunyan Yang , Liang Zhao

In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…

Numerical Analysis · Mathematics 2026-03-04 Lukas Pflug , Michael Stingl , Max Zetzmann

We obtain the local well-posedness for Dirac equations with a Hartree type nonlinearity derived by decoupling the Dirac-Klein-Gordon system. We extend the function space of initial data, enabling us to handle initial data that were not…

Analysis of PDEs · Mathematics 2024-12-03 Seongyeon Kim , Hyeongjin Lee , Ihyeok Seo

The Perona-Malik equation is a celebrated example of forward-backward parabolic equation. The forward behavior takes place in the so-called subcritical region, in which the gradient of the solution is smaller than a fixed threshold. In this…

Analysis of PDEs · Mathematics 2009-09-02 Marina Ghisi , Massimo Gobbino

The famous Perona-Malik (P-M) equation which was at first introduced for image restoration has been solved via various numerical methods. In this paper we will solve it for the first time via applying a new numerical method called Homotopy…

Computer Vision and Pattern Recognition · Computer Science 2010-08-17 Keyvan Yahya , Jafar Biazar , Hossein Azari , Pouyan Rafiei Fard
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