一类带漂移-扩散项的非线性抛物型方程组的能控性

Abstract

Abstract:

This paper studies the controllability and the existence of time optimal control for a class of nonlinear parabolic equations, which has drift-diffusion term with nonlinear terms $h(u,v)$ and $g(u,v)$. It applies the $L^{p}$-$L^{q}$ estimate of semigroups and the recently developed maximal regularity theory to study the regularity and the cost estimate of control functions. Moreover, this paper establishes the local exact controllability of the nonlinear control system by utilizing the Kakutani's fixed point theorem. Therefore, it is applied to the existence of time optimal controls.

Key words: Parabolic equations, Observability estimate, Exact controllability, Kakutani's fixed point

CLC Number:

O231.4

Zhang Zhipeng, Zhang Liang. Controllability of a Nonlinear Parabolic Systems with Drift-Diffusion Term[J].Acta mathematica scientia,Series A, 2023, 43(6): 1744-1758.

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References

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Controllability of a Nonlinear Parabolic Systems with Drift-Diffusion Term

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