We consider initial boundary value problem for the time–space fractional parabolic–elliptic Keller–Segel model 0CDtβu=−(−Δ)α2(ρ(v)u),(t,x)∈(0,T]×Ω(−Δ)α2v+v=u,(t,x)∈(0,T]×Ωin a bounded domain Ω⊂Rn(n≥3) with smooth boundary, where β∈(0,1),α∈(1,2) and ρ stands signal-dependent motility. It is shown that some special datum, there exists uniform-in-time upper bound v such associated initial–boundary...

In this paper, KdV-type equations with time- and space-dependent coefficients are considered. Assuming that the dispersion coefficient in front of $$ u_{xxx} is positive uniformly bounded away from zero a primitive function ratio between anti-dissipation below, we prove existence uniqueness solution u such hu belongs to classical Sobolev space, where h related ratio. The LWP H^s({\mathbb {R}}) ...

According to biological strategy for pest control, we investigate the dynamic behavior of a pest management SEI model with nonlinear incidence concerning impulsive strategyperiodic releasing infected pests at fixed times. We prove that all solutions of the system are uniformly ultimately bounded and there exists a globally asymptotically attractive pest-eradication periodic solution when the im...

Almost transitive superreflexive Banach spaces have been considered in [7] (see also [4] and [6]), where it is shown that such spaces are uniformly convex and uniformly smooth. We prove that convex transitive Banach spaces are either almost transitive and superreflexive (hence uniformly smooth) or extremely rough. The extreme roughness of a Banach space X means that, for every element u in the ...

The purpose of this paper is to consider an iterative method for an equilibrium problem and a family relatively nonexpansive mappings. Weak convergence theorems are established in uniformly smooth and uniformly convex Banach spaces.

We prove several decidability and undecidability results for ν-PN, an extension of P/T nets with pure name creation and name management. We give a simple proof of undecidability of reachability, by reducing reachability in nets with inhibitor arcs to it. Thus, the expressive power of ν-PN strictly surpasses that of P/T nets. We prove that ν-PN are Well Structured Transition Systems. In particul...

0. Introduction 1 1. Standard definitions 3 2. Examples 4 3. Some methods for proving boundedness 8 4. Additional definitions and easy technical results 9 5. The diagram method 10 6. Boundedness for surfaces with nef −(K+B) 14 7. Boundedness for surfaces with big and nef K +B 18 8. Descending Chain Condition 23 9. Boundedness for the constant (K +B)2 27 10. On log MMP for surfaces 28 11. Conclu...

In this letter, we consider the ultimate boundedness of the singularly perturbed system with measurement noise. The composite controller is commonly used to regulate the singularly perturbed system. However, in the presence of measurement noise, the composite controller does not guarantee the ultimate boundedness of the singularly perturbed system. Thus, we propose the modified composite contro...