In this article, the globally bounded in-time pointwise estimate of solutions to the simplified Keller-Segel system modelling chemotaxis are derived. Moreover, a local existence theorem is obtained.
In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="&q...In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="" />(0.1)<br /> <p> is considered in a bounded domain with smooth boundary, Ω ⊂R<sup><i>n</i></sup> (<i>n</i> ≥ 1), where <i>d</i><sub>1</sub> > 0, <i>d</i><sub>2</sub> > 0 with parameter <i>χ</i> ∈ R. When <i>d</i><sub>1</sub> = <i>d</i><sub>2</sub> + <i>χ</i>, satisfying for all initial data 0 ≤ <i>n</i><sub>0</sub> ∈ <i>C</i><sup>0</sup><img src="Edit_4898c7a9-f047-4856-b9ad-8d42ecf262a2.bmp" alt="" /> and 0 < <i>v</i><sub>0</sub>∈ <i>W</i><sup>1,∞</sup> (Ω), we prove that the problem possesses a unique global classical solution which is uniformly bounded in Ω × (0, ∞). </p>展开更多
A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and...A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and a novel filtered tracking error,capable of compensating for input delays.Suitable Lyapunov-Krasovskii functionals are used to prove global uniformly ultimately bounded(GUUB)tracking,provided certain sufficient gain conditions,dependent on the bound of the delay,are satisfied.Simulation results illustrate the performance and robustness of the controller for different values of input delay.展开更多
In this paper,we investigate the global complexity bound for the inexact Levenberg–Marquardt method,where the Jacobian may be perturbed and the solution is possibly not exact.Under reasonable assumptions,we show that...In this paper,we investigate the global complexity bound for the inexact Levenberg–Marquardt method,where the Jacobian may be perturbed and the solution is possibly not exact.Under reasonable assumptions,we show that the global complexity bound is O(ε^(−2)),which is the same as the exact case.We also show that it can be reduced to O(lgε^(−1))under some regularity assumption.展开更多
基金Supported by the NSF of Jiangxi Province, the NSFC (10225105, 10671023) and a CAEP grant
文摘In this article, the globally bounded in-time pointwise estimate of solutions to the simplified Keller-Segel system modelling chemotaxis are derived. Moreover, a local existence theorem is obtained.
文摘In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="" />(0.1)<br /> <p> is considered in a bounded domain with smooth boundary, Ω ⊂R<sup><i>n</i></sup> (<i>n</i> ≥ 1), where <i>d</i><sub>1</sub> > 0, <i>d</i><sub>2</sub> > 0 with parameter <i>χ</i> ∈ R. When <i>d</i><sub>1</sub> = <i>d</i><sub>2</sub> + <i>χ</i>, satisfying for all initial data 0 ≤ <i>n</i><sub>0</sub> ∈ <i>C</i><sup>0</sup><img src="Edit_4898c7a9-f047-4856-b9ad-8d42ecf262a2.bmp" alt="" /> and 0 < <i>v</i><sub>0</sub>∈ <i>W</i><sup>1,∞</sup> (Ω), we prove that the problem possesses a unique global classical solution which is uniformly bounded in Ω × (0, ∞). </p>
文摘A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and a novel filtered tracking error,capable of compensating for input delays.Suitable Lyapunov-Krasovskii functionals are used to prove global uniformly ultimately bounded(GUUB)tracking,provided certain sufficient gain conditions,dependent on the bound of the delay,are satisfied.Simulation results illustrate the performance and robustness of the controller for different values of input delay.
基金This work was partially supported by the National Natural Science Foundation of China(No.11571234).
文摘In this paper,we investigate the global complexity bound for the inexact Levenberg–Marquardt method,where the Jacobian may be perturbed and the solution is possibly not exact.Under reasonable assumptions,we show that the global complexity bound is O(ε^(−2)),which is the same as the exact case.We also show that it can be reduced to O(lgε^(−1))under some regularity assumption.
