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The Winfree model is a phase-coupled synchronization model which simplifies pulse-coupled models such as the Peskin model on pacemaker cells. It is well-known that the Winfree ensemble with the first-order coupling exhibits discrete asymptotic patterns such as incoherence, locking and death...
In this paper we study solutions, possibly unbounded and sign-changing, of a weighted static Choquard equation involving the Grushin operator. Under some appropriate assumptions on the parameters, we prove various Liouville-type theorems for weak solutions under the assumption that they are...
This paper studies the efficiency of protection in containing an epidemic in the case of immigration using a triple age structured model. For determining this efficiency, we split our study into two different cases, (i) with immigration flow into all model classes, (ii) without infected...
In this remark, we consider regularity criterion for weak solutions to the 3d incompressible Navier–Stokes equations via pressure. It is proved that if the corressponding pressure...
In this paper, we systematically study two-species reaction-diffusion-advection system with linear cross-diffusion and cross-advection. Firstly, we provide sufficient conditions for cross-diffusion, self-advection and cross-advection driven instability, which implies that cross-diffusion,...
This work is devoted to presenting Massera-type theorems for the Kawahara system, a higher-order dispersive equation, posed in a bounded domain. Precisely, thanks to some properties of the semigroup and the decay of the solutions of this equation, we can prove its solutions are periodic,...
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