In this present paper, we deal with a generalized Lengyel–Epstein model with the zero-flux
boundary conditions. Firstly, we give an attraction region and the boundedness estimates of …

We study the existence, nonexistence and asymptotics of positive solutions to the Gierer–
Meinhardt system-Δ u+ λ u= upvq+ ρ (x), u> 0 in R+ N:= RN-1×(0,∞),-Δ v+ λ v= umvs, v> 0 in …

In this paper, we provide a thorough investigation of the blowing up behavior induced via
diffusion of the solution of the following non-local problem:∂ tu= Δ u− u+ up∫ Ω urdr γ in …

In the current work, we study a stochastic parabolic problem. The presented problem is
motivated by the study of an idealised electrically actuated MEMS (Micro-Electro-Mechanical …

We consider a nonlocal parabolic PDE, which may be regarded as the standard semilinear
heat equation with power nonlinearity, where the nonlinear term is divided by some Sobolev …

In this paper, we consider the existence of spike stationary solutions for the Gierer-Meinhardt
model with advection term on the Y-shaped metric graph. By using Liapunov-Schmidt …

We study the transmission dynamics of a fecal-oral diseases model on a T-periodic
evolution domain. We introduce the basic reproduction number R0 (ρ) as a threshold by …

In this paper, we study the existence of spiky stationary solutions for reaction-diffusion-
advection systems on the Y-shaped metric graph. Considering the Schnakenberg chemical …

We discuss the existence and nonexistence of solutions to the steady-state Gierer-Meinhardt
system $$\begin {cases}\displaystyle-\Delta u=\frac {u^ p}{v^ q}+\lambda\rho (x)\,, u> 0 …

The purpose of the current paper is to unveil the key mechanism which is responsible for the
occurrence of Turing-type instability for a nonlocal Fisher-KPP model. In particular, we prove …