This paper is concerned with the bistable wave fronts of integrodifference equations. The existence, uniqueness, and asymptotic stability of bistable wave fronts for such an equation are proved by the squeezing technique based on comparison principle.
Abstract. A type of delayed Lotka-Volterra competition reaction-diffusion system is considered. By constructing a new Lyapunov function, we prove that the unique positive steady-state solution is globally asymptotically stable when interspecies competition is weaker than intraspecies competition. Moreover, we show that the stability property does not depend on the diffusion coefficients and time delays.
a b s t r a c tWe provide a sufficient condition for the regularity of solutions to the 3D nematic liquid crystal flow in the Morrey-Campanato space. More precisely, we prove that if the velocity u satisfies3 r , or the gradient of the velocity ∇u satisfies T 0 ∥∇u(·, t)∥ 2 2−γ M p, 3 γ 1 + ln(e + ∥u(·, t)∥ L 6 ) dt < ∞ with 0 < γ ≤ 1 and 2 ≤ p ≤ 3 γ , then the solution (u, d) remains smooth on (0, T ].Crown
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