Related papers: Hyperbolic Relaxation of Reaction Diffusion Equati…
This paper investigates solutions of hyperbolic diffusion equations in $\mathbb{R}^3$ with random initial conditions. The solutions are given as spatial-temporal random fields. Their restrictions to the unit sphere $S^2$ are studied. All…
In this paper we study the existence, the optimal regularity of solutions, and the regularity of the free boundary near the so-called \emph{regular points} in a thin obstacle problem that arises as the local extension of the obstacle…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
We prove well posedness and stability in $\mathbf{L}^1$ for a class of mixed hyperbolic-parabolic non linear and non local equations in a bounded domain with no flow along the boundary. While the treatment of boundary conditions for the…
A popular approach to modeling bimolecular reactions between diffusing molecules is through the use of reactive boundary conditions. One common model is the Smoluchowski partial absorption condition, which uses a Robin boundary condition in…
In this paper, we consider the pointwise boundary Lipschitz regularity of solutions for the semilinear elliptic equations in divergence form mainly under some weaker assumptions on nonhomogeneous term and the boundary. If the domain…
Global dynamics of the diffusive Hindmarsh-Rose equations with memristor as a new proposed model for neuron dynamics are investigated in this paper. We prove the existence and regularity of a global attractor for the solution semiflow…
We consider an initial boundary value problem for a quantum version of the Zakharov system arising in plasma physics. We prove the global well-posedness of this problem in some Sobolev type classes and study properties of solutions. This…
We prove existence, uniqueness, and regularity for a reaction-diffusion system of coupled bulk-surface equations on a moving domain modelling receptor-ligand dynamics in cells. The nonlinear coupling between the three unknowns is through…
This paper concerns the asymptotics of certain parabolic-elliptic chemotaxis-consumption systems with logistic growth and constant concentration of chemoattractant on the boundary. First we prove that in two dimensional bounded domains…
We prove existence of strong solutions to a family of some semilinear parabolic free boundary problems by means of elliptic regularization. Existence of solutions is obtained in two steps: we first show some uniform energy estimates and…
This paper is concerned with boundary stabilization of two-dimensional hyperbolic systems of partial differential equations. By adapting the Lyapunov function previously proposed by the second author for linearized hyperbolic systems with…
We study the well-posedness of a nonlinear reaction diffusion partial differential equation system on the half-line coupled with a stochastic dynamical boundary condition, a random system arising from the description of the chemical…
We consider a class of reaction-diffusion equations with a stochastic perturbation on the boundary. We show that in the limit of fast diffusion, one can rigorously approximate solutions of the system of PDEs with stochastic Neumann boundary…
We consider steady-state diffusion in a bounded planar domain with multiple small targets on a smooth boundary. Using the method of matched asymptotic expansions, we investigate the competition of these targets for a diffusing particle and…
The purpose of this paper is to investigate the existence and estimation of Hausdorff and fractal dimension of global attractors for a delayed reaction-diffusion equation on an unbounded domain. The noncompactness of the domain cause the…
We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish local…
We investigate global bounded solutions of higher regularity to boundary value problems for a general linear nonautonomous first order 1D hyperbolic system in a strip. We establish the existence of such solutions under the assumption of…
Linear reaction-diffusion equations with inhomogeneous boundary and transmission conditions are shown to possess the property of maximal Lp regularity. The new feature is the fact that the transmission interface is allowed to intersect the…
We prove the existence and uniqueness of tempered random attractors for stochastic Reaction-Diffusion equations on unbounded domains with multiplicative noise and deterministic non-autonomous forcing. We establish the periodicity of the…