Related papers: A non-local quenching system with coupled and unco…
We show well-posedness of a diffuse interface model for a two-phase flow of two viscous incompressible fluids with different densities locally in time. The model leads to an inhomogeneous Navier-Stokes/Cahn-Hilliard system with a solenoidal…
We study the quasilinear non-local Benney System $$\left\{\begin{array}{llll} iu_t+u_{xx}=|u|^2u+buv\\ v_t+a(\int_{\mathbf{R}^+}v^2dx)v_x=-b(|u|^2)_x,\quad (x,t)\in\mathbf{R}^+\times [0,T],\, T>0. \end{array}\right.$$ We establish the…
We investigate a system describing the flow of a compressible two-component mixture. The system is composed of the compressible Navier-Stokes equations coupled with non-symmetric reaction-diffusion equations describing the evolution of…
We consider a non-Hermitian medium with a gain and loss symmetric, exponentially damped potential distribution to demonstrate different scattering features analytically. The condition for critical coupling (CC) for unidirectional wave and…
We consider a large class of nonlinear diffusive systems with nonlocal coupling. By using a non-perturbative analytical approach we are able to determine the convective and absolute instabilities of all the uniform states of these systems.…
We previously showed that a quantum quench in a one-dimensional translation invariant system produces undamped oscillations of a local observable when the post-quench state includes a single-quasiparticle mode and the observable couples to…
The paper deals with the existence of solutions for quasilinear elliptic systems involving singular and convection terms with variable exponents. Our approach combines the sub-supersolutions method and Schauder's fixed point theorem.
A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary…
We study problems in which a local model is coupled with a nonlocal one. We propose two energies: both of them are based on the same classical weighted $H^1$-semi norm to model the local part, while two different weighted $H^s$-semi norms,…
A microscopic model of adsorption in cluster forming systems with competing interaction is considered. The adsorption process is described by the master equation and modelled by a kinetic Monte Carlo method. The evolution of the particle…
In this paper we consider a porous-elastic system consisting of nonlinear boundary/interior damping and nonlinear boundary/interior sources. Our interest lies in the theoretical understanding of the existence, finite time blow-up of…
We prove an existence result for nonlinear diffusion equations in the presence of a nonlocal density-dependent drift which is not necessarily potential. The proof is constructive and based on the Helmholtz decomposition of the drift and a…
In this work, we study the existence and nonexistence of nonnegative solutions to a class of nonlocal elliptic systems set in a bounded open subset of $\mathbb{R}^N$. The diffusion operators are of type $u_i\mapsto d_i(-\Delta)^{s_i}u_i$…
In this paper we consider a subcritical model that involves nonlocal diffusion and a classical convective term. In spite of the nonlocal diffusion, we obtain an Oleinik type estimate similar to the case when the diffusion is local. First we…
We set up and study a coupled problem on stationary non-isothermal flow of electrorheological fluids. The problem consist in finding functions of velocity, pressure and temperature which satisfy the motion equations, the condition of…
Solving the stationary nonlinear Fokker-Planck equations is important in applications and examples include the Poisson-Boltzmann equation and the two layer neural networks. Making use of the connection between the interacting particle…
We prove a contraction in $L^1$ property for the solutions of a nonlinear reaction--diffusion system whose special cases include intercellular transport as well as reversible chemical reactions. Assuming the existence of stationary…
Elastic interfaces embedded in (quenched) random media exhibit meta-stability and stick-slip dynamics. These non-trivial dynamical features have been shown to be associated with cusp singularities of the coarse-grained disorder correlator.…
This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…
In this paper we propose and validate a multiscale model for the description of particle diffusion in presence of trapping boundaries. We start from a drift-diffusion equation in which the drift term describes the effect of bubble traps,…