This paper is concerned with the blowup phenomenon of stochastic parabolic equations both on bounded domain and in whole space. We introduce a new method to study domain. Compared existing results, we delete assumption that solutions heat are nonnegative. Then space obtained by using properties kernel. obtain will blow up finite time for nontrivial initial data.

This paper is concerned with the entire solution of a diffusive and competitive Lotka–Volterra type system nonlocal delays. The existence proved by transforming delays to four-dimensional without delay using comparing argument sub-super-solution method. Here an means classical defined for all space time variables, which behaves as two wave fronts coming from both sides x-axis.

ABSTRACT In this paper, we investigate the dynamic behavior of a criminal model (predator–prey model), in which predators are police, and prey is gang members, both have infectious diseases, infected being more susceptible to predation, hunting at reduced rate. We get sufficient criteria for existence uniqueness an ergodic stationary distribution positive solutions system by establishing series suitable Lyapunov functions. biological viewpoint, indicates that police members will be...

This paper deals with the nonlinear stability of travelling wave fronts for delayed reaction diffusion equations. We prove that are exponentially stable to perturbations in some weighted L∞ spaces, and obtain time decay rates by energy estimate.

In this paper, some new blow-up criteria are given for a single equation, and the problem of solution nonlocal equation is solved by changing into system equations introducing an auxiliary function. addition, theory ordinary differential extended to partial using first eigenvalue theory. The results show that Liouville-Caputo Caputo-Hadamard fractional different.

The aim of this paper is to establish the averaging principle for stochastic differential equations under a general condition, which weaker than traditional case. Under we an effective approximation solution in mean square.

This paper is concerned with the non-uniform dependence on initial data for a modified Camassa-Holm system. We prove that solution map of Cauchy problem system not uniformly continuous in \documentclass[12pt]{minimal}\begin{document}$H^s(\mathbb {R})$\end{document}Hs(R), s > 1. Moreover, we obtain similar result boundary value

We introduce a new inequality similar to the fractional Poincar$ \acute{e} $ and obtain continuous data assimilation feedback control of reaction-diffusion equations. The scheme has finite number determining parameters. is obtained based on finite-dimensional controls.

This paper proposes a fishery model with price fluctuations and predators. Under the assumption that changes much faster than other variables in system, can be considered as fast–slow system. Using approximate aggregation method, simplified three-dimensional is used for further research. The results indicate due to overfishing by fishermen presence of predators, fish populations may become extinct, which also known catastrophic equilibrium. To avoid this situation, we propose two solutions....

This paper is concerned with the asymptotic stability of planar waves in mono-stable reaction-diffusion equations $\mathbb {R}^n$, where $n\geq 2$. Under initial perturbation that decays at space infinity, perturbed solution converges to as $t\rightarrow \infty$. The convergence uniform {R}^n$.

In this paper, we are concerned with a rumor propagation model L vy noise. We first prove that there exists positive global solution. Then, the asymptotic behaviors around rumor‐free equilibrium and rumor‐epidemic obtained. Lastly, simulations verify our results.