相关论文: All Invariant Regions and Global Solutions for m-c…

We introduce an extension of the concept of renormalised solutions for entropy-dissipating reaction-diffusion systems due to J. Fischer (Arch. Ration. Mech. Anal. 218, 2015) to systems coupled by nonlinear interface conditions. For this…

We consider asymptotic problems concerning the motion of interface separating the regions of large and small values of the solution of a reaction-diffusion equation in the media consisting of domains with different characteristics…

The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at multi-frequencies. The data are generated…

In this work, we investigate the dynamical properties of a reaction-diffusion system arising from tumor-therapy modelling that features both nonlinear interactions and nonlocal delay. By applying the Lyapunov-Schmidt reduction, we establish…

We consider the inverse problem of determining a general semilinear term appearing in nonlinear parabolic equations. For this purpose, we derive a new criterion that allows to prove global recovery of some general class of semilinear terms…

Although the spatially continuous version of the reaction-diffusion equation has been well studied, in some instances a spatially-discretized representation provides a more realistic approximation of biological processes. Indeed,…

Volume-filling cross-diffusion equations for the components of a tissue structure are formally derived from mass conservation laws and force balances for the interphase pressures and viscous drag forces in a multiphase approach. The…

The aim of this paper is to establish convergence, properties and error bounds for the fully discrete solutions of a class of nonlinear systems of reaction-diffusion nonlocal type with moving boundaries, using the finite element method with…

Following the approach pioneered by Eckhaus, Mielke, Schneider, and others for reaction diffusion systems [E, M1, M2, S1, S2, SZJV], we systematically derive formally by multiscale expansion and justify rigorously by Lyapunov-Schmidt…

In this study, the numerical solutions of reaction-diffusion systems are investigated via the trigonometric quintic B-spline nite element collocation method. These equations appear in various disciplines in order to describe certain…

This paper investigates a class of novel nonlinear reaction-diffusion systems that couple forward-backward with fractional diffusion for image restoration, offering the advantage of preserving both contour features and textures. The…

We consider Fisher-KPP-type reaction-diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-front-type global in time solutions while…

Exact solutions for nonlinear Arrhenius reaction-diffusion are constructed in $n$ dimensions. A single relationship between nonlinear diffusivity and the nonlinear reaction term leads to a nonclassical Lie symmetry whose invariant solutions…

We study the Cauchy problem for a system of semi-linear coupled fractional-diffusion equations with polynomial nonlinearities posed in $% \mathbb{R}_{+}\times \mathbb{R}^{N}$. Under appropriate conditions on the exponents and the orders of…

Two important classes of spatio-temporal patterns, namely, spatio-temporal chaos and self-replicating patterns, for a representative three variable autocatalytic reaction mechanism coupled with diffusion has been studied. The…

High-dimensional fractional reaction-diffusion equations have numerous applications in the fields of biology, chemistry, and physics, and exhibit a range of rich phenomena. While classical algorithms have an exponential complexity in the…

We introduce and study the first model of an experimentally realizable three-dimensional time-dependent nonturbulent fluid flow to display the phenomenon of global diffusion of passive-scalar particles at arbitrarily small values of the…

We study the uniqueness of reaction-diffusion steady states in general domains with Dirichlet boundary data. Here we consider "positive" (monostable) reactions. We describe geometric conditions on the domain that ensure uniqueness and we…

It is well-known that one-dimensional time fractional diffusion-wave equations with variable coefficients can be reduced to ordinary fractional differential equations and systems of linear fractional differential equations via scaling…

We develop a theory describing the transition to a spatially homogeneous regime in a mixing flow with a chaotic in time reaction. The transverse Lyapunov exponent governing the stability of the homogeneous state can be represented as a…