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Reaction-diffusion systems have been primary tools for studying pattern formation. A skew-gradient system is well known to encompass a class of activator-inhibitor type reaction-diffusion systems that exhibit localized patterns such as…

Analysis of PDEs · Mathematics 2019-10-31 Yung-Sze Choi , Jieun Lee

This paper is concerned with reaction-diffusion-advection equations in spatially periodic media. Under an assumption of weak stability of the constant states 0 and 1, and of existence of pulsating traveling fronts connecting them, we show…

Analysis of PDEs · Mathematics 2026-04-14 Hongjun Guo , François Hamel , Luca Rossi

We propose a new variational approach to finding multiple critical points for strongly indefinite problems without assuming the weak upper semicontinuity on the variational functionals. By this approach, we obtain the existence of…

Functional Analysis · Mathematics 2024-04-04 Long-Jiang Gu , Huan-Song Zhou

In this paper we describe invariant geometrical ~structures in the phase space of the Swift-Hohenberg equation in a neighborhood of its periodic stationary states. We show that in spite of the fact that these states are only marginally…

patt-sol · Physics 2009-10-30 J. -P. Eckmann , C. E. Wayne , P. Wittwer

A wave front and a wave back that spontaneously connect two hyperbolic equilibria, known as a heteroclinic wave loop, give rise to periodic waves with arbitrarily large spatial periods through the heteroclinic bifurcation. The nonlinear…

Analysis of PDEs · Mathematics 2025-03-28 Ji Li , Ke Wang , Qiliang Wu , Qing Yu

In this paper we study pattern formation arising in a system of a single reaction-diffusion equation coupled with subsystem of ordinary differential equations, describing spatially-distributed growth of clonal populations of precancerous…

Tissues and Organs · Quantitative Biology 2019-05-14 Yuriy Golovaty , Anna Marciniak-Czochra , Mariya Ptashnyk

This paper jointly addresses the challenges of non-stationarity and high dimensionality in analysing multivariate time series. Building on the classical concept of cointegration, we introduce a more flexible notion, called stability space,…

We consider reaction-diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, coloured in space, and invariant under translations. In the deterministic setting,…

Analysis of PDEs · Mathematics 2024-06-07 Mark van den Bosch , Hermen Jan Hupkes

In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that connect the trivial equilibrium, for which all components of…

Analysis of PDEs · Mathematics 2025-11-14 Liangliang Deng , Arnaud Ducrot , Quentin Griette

In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…

Numerical Analysis · Mathematics 2013-08-05 Erik Burman

In this paper we give a systematic and simple account that put in evidence that many breather solutions of integrable equations satisfy suitable variational elliptic equations, which also implies that the stability problem reduces in some…

Mathematical Physics · Physics 2016-04-29 Miguel A. Alejo , Claudio Muñoz , José M. Palacios

We prove the existence of infinitely many classical periodic solutions for a class of semilinear wave equations with periodic boundary conditions. Our argument relies on some new estimates for the linear problem with periodic boundary…

Analysis of PDEs · Mathematics 2011-04-07 Jean Marcel Fokam

This paper focuses on the numerical stability of stochastic McKean-Vlasov equations (SMVEs) via the stochastic particle method. Firstly, the long-time propagation of chaos in the mean-square sense is obtained, and the almost sure…

Numerical Analysis · Mathematics 2025-08-04 Zhuoqi Liu , Shuaibin Gao , Chenggui Yuan , Qian Guo

We present high signal-to-noise ratio, multi-frequency polarization pulse profiles for 24 millisecond pulsars that are being observed as part of the Parkes Pulsar Timing Array (PPTA) project. The pulsars are observed in three bands, centred…

For perturbations of integrable Hamiltonians systems, the Nekhoroshev theorem shows that all solutions are stable for an exponentially long interval of time, provided the integrable part satisfies a steepness condition and the system is…

Dynamical Systems · Mathematics 2015-05-20 Abed Bounemoura

The paper introduces and studies the notions of Lipschitzian and H\"olderian full stability of solutions to three-parametric variational systems described in the generalized equation formalism involving nonsmooth base mappings and partial…

Optimization and Control · Mathematics 2017-08-23 Boris S. Mordukhovich , Tran T. A. Nghia , Dat T. Pham

Proposed to study the dynamics of physiological systems in which the evolution depends on the state in a previous time, the Mackey-Glass model exhibits a rich variety of behaviors including periodic or chaotic solutions in vast regions of…

Disordered Systems and Neural Networks · Physics 2021-12-22 Juan P. Tarigo , Cecilia Stari , Cecilia Cabeza , Arturo C. Marti

We study linear stability of exponential periodic solutions of a system of singular amplitude equations associated with convective Turing bifurcation in the presence of conservation laws, as arises in modern biomorphology models, binary…

Analysis of PDEs · Mathematics 2025-07-01 Aric Wheeler , Kevin Zumbrun

We study the existence of polychromatic solutions of cubically nonlinear Maxwell equations in the whole space and with dispersive media, i.e., with a time delayed polarization. Due to the complex nature of the dielectric function, the…

Analysis of PDEs · Mathematics 2025-11-27 Tomas Dohnal , Maximilian Hanisch , Runan He

We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…

Analysis of PDEs · Mathematics 2024-04-23 Faouzi Triki , Kristoffer Linder-Steinlein , Mirza Karamehmedovic