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A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial…

Analysis of PDEs · Mathematics 2023-04-14 Szymon Cygan , Grzegorz Karch , Anna Marciniak-Czochra , Kanako Suzuki

This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…

Numerical Analysis · Mathematics 2025-05-07 Xu Wu , Jiang Yang , Zhi Zhou

We consider a family of conforming space-time finite element discretizations for the wave equation based on splines of maximal regularity in time. Traditional techniques may require a CFL condition to guarantee stability. Recent works by O.…

Numerical Analysis · Mathematics 2024-10-25 Matteo Ferrari , Sara Fraschini

We consider split-step Milstein methods for the solution of stiff stochastic differential equations with an emphasis on systems driven by multi-channel noise. We show their strong order of convergence and investigate mean-square stability…

Numerical Analysis · Mathematics 2014-11-27 V. Reshniak , A. Q. M. Khaliq , D. A. Voss , G. Zhang

In this paper, the problem of stability in terms of two measures is considered for a class of stochastic partial differential delay equations with switching. Sufficient conditions for stability in terms of two measures are obtained based on…

Dynamical Systems · Mathematics 2016-09-07 Shufen Zhao , Minghui Song

We investigate the dynamics of dissipative systems with stochastic forcing and focus in particular on mean-square stability. First we show, under a natural condition on the drift and diffusion, that the stochastic system is mean-square…

Probability · Mathematics 2026-05-01 C. Kelly , G. J. Lord , M. Ptashnyk , S. Sonner

For solving unsteady hyperbolic conservation laws on cut cell meshes, the so called small cell problem is a big issue: one would like to use a time step that is chosen with respect to the background mesh and use the same time step on the…

Numerical Analysis · Mathematics 2019-12-30 Florian Streitbürger , Christian Engwer , Sandra May , Andreas Nüßing

Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…

Numerical Analysis · Mathematics 2024-01-30 Anindya Goswami , Kuldip Singh Patel , Pradeep Kumar Sahu

Following the approach of [E1, M1, M2, S1, S2, SZJV] for reaction diffusion systems, we justify rigorously the Eckhaus stability criterion for stability of convective Turing patterns, as derived formally by complex Ginzburg-Landau…

Dynamical Systems · Mathematics 2025-06-30 Aric Wheeler , Kevin Zumbrun

Based on the generalized Routh-Hurwitz criterion, we propose a sufficient and necessary criterion for testing the stability of fractional-order linear systems with order {\alpha}{\in}[1,2), called the fractional-order Routh-Hurwitz…

Dynamical Systems · Mathematics 2022-02-22 Jing Yang , Xiaorong Hou , Yajun Li

We revisit the diffusive instability in dusty disks that arises when the dust mass diffusivity and/or viscosity decreases sufficiently steeply with increasing dust density. Our updated model includes an incompressible, viscous gas that…

Earth and Planetary Astrophysics · Physics 2026-02-19 Konstantin Gerbig , Min-Kai Lin

In this paper, we present sufficient conditions for asymptotic stability and exponential stability of a class of impulsive neutral differential equations with discrete and distributed delays. Our approaches are based on the method using…

Dynamical Systems · Mathematics 2025-04-03 Jinyuan Pan , Guiling Chen

We prove stability results for nonlinear diffusion equations of the porous medium and fast diffusion types with respect to the nonlinearity power $m$: solutions with fixed data converge in a suitable sense to the solution of the limit…

Analysis of PDEs · Mathematics 2013-09-04 Teemu Lukkari

We consider a stabilization method for divergence-conforming B-spline discretizations of the incompressible Navier--Stokes problem wherein jumps in high-order normal derivatives of the velocity field are penalized across interior mesh…

Numerical Analysis · Mathematics 2022-01-28 Guoxiang Grayson Tong , David Kamensky , John A. Evans

We develop a stabilized cut finite element method for the stationary convection diffusion problem on a surface embedded in ${\mathbb{R}}^d$. The cut finite element method is based on using an embedding of the surface into a three…

Numerical Analysis · Mathematics 2018-07-24 Erik Burman , Peter Hansbo , Mats G. Larson , Andre Massing , Sara Zahedi

We consider random perturbations of discrete-time dynamical systems. We give sufficient conditions for the stochastic stability of certain classes of maps, in a strong sense. This improves the main result in J. F. Alves, V. Araujo, Random…

Dynamical Systems · Mathematics 2010-03-01 Jose F. Alves , Helder Vilarinho

We investigate dynamics near Turing patterns in reaction-diffusion systems posed on the real line. Linear analysis predicts diffusive decay of small perturbations. We construct a "normal form" coordinate system near such Turing patterns…

Analysis of PDEs · Mathematics 2015-10-29 Arnd Scheel , Qiliang Wu

As the main contribution, this document provides a consistent discretization of a class of fixed-time stable systems, namely predefined-time stable systems. In the unperturbed case, the proposed approach allows obtaining not only a…

In this paper the linear and stationary Discrete-time systems with state variables and dynamic coefficients represented by fuzzy numbers are studied, providing some stability criteria, and characterizing the bounds of the set of solutions…

Systems and Control · Computer Science 2011-09-05 Gabriele Oliva , Stefano Panzieri , Roberto Setola

This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…

Probability · Mathematics 2023-05-22 Taras Lukashiv , Igor V. Malyk , Maryna Chepeleva , Petr V. Nazarov