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We investigate the Cahn-Hilliard equation with nonlinear diffusion and non-degenerate mobility modeling phase separation phenomena in complex systems (e.g., crystals and polymers). Previous results in the literature on this model relied on…

We introduce a multimodel approach to the simulation of the optical properties of molecular dyes in solution, whereby the effects of thermal fluctuations and of dielectric screening on the absorption spectra are accounted for by explicit…

The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…

Parametrized polynomial ordinary differential equation systems are broadly used for modeling, specially in the study of biochemical reaction networks under the assumption of mass-action kinetics. Understanding the qualitative behavior of…

We study an alloy system where short-ranged, thermally-driven diffusion competes with externally imposed, finite-ranged, athermal atomic exchanges, as is the case in alloys under irradiation. Using a Cahn-Hilliard-type approach, we show…

We consider the class of dissipative reaction-diffusion-convection systems on the circle and obtain conditions under which the final (at large times) phase dynamics of a system can be described by an ODE with Lipschitz vector field in…

We investigate the time evolution of the decay (or ionization) probability of a D-dimensional model atom (D=1,2,3) in the presence of a uniform (i.e., static and homogeneous) background field. The model atom consists in a non-relativistic…

Many types of spatiotemporal patterns have been observed under nonequilibrium conditions. Cycling through four or more states can provide specific dynamics, such as the spatial coexistence of multiple phases. However, transient dynamics…

We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the neutral phase, we prove that spatially localized perturbations…

Non-linear behavior in interstellar chemical models has been recognized for 25 years now. Different mechanisms account for the possibility of multiple fixed-points at steady state, characterized by the ionization degree of the gas. Chemical…

This paper presents a nonlinear dynamical model which consists the system of differential and operator equations. Here differential equation contains a nonlinear operator acting in Banach space, a nonlinear operator equation with respect to…

We investigate limit models resulting from a dimensional analysis of quite general heterogeneous catalysis models with fast sorption (i.e.\ exchange of mass between the bulk phase and the catalytic surface of a reactor) and fast surface…

We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assumption, prove that it implies nonlinear stability and provide…

Complex systems, which consist of a large number of interacting constituents, often exhibit universal behavior near a phase transition. A slowdown of certain dynamical observables is one such recurring feature found in a vast array of…

Consider the Cauchy problem for a nonlinear diffusion equation \begin{equation} \tag{P} \left\{ \begin{array}{ll} \partial_t u=\Delta u^m+u^\alpha & \quad\mbox{in}\quad{\bf R}^N\times(0,\infty),\\ u(x,0)=\lambda+\varphi(x)>0 &…

Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…

We consider a third order non-autonomous ODE that arises as a model of fluid accumulation in a two dimensional thin-film flow driven by surface tension and gravity. With the appropriate matching conditions, the equation describes the inner…

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…

Motivated by the possibility of electrochemical control of phase separation, a variational theory of thermodynamic stability is developed for driven reactive mixtures, based on a nonlinear generalization of the Cahn-Hilliard and Allen-Cahn…

The periodic $Z_n$-Belavin model on a lattice with an arbitrary number of sites $N$ is studied via the off-diagonal Bethe Ansatz method (ODBA). The eigenvalues of the corresponding transfer matrix are given in terms of an unified…