Regularity Analysis for an Abstract System of Coupled Hyperbolic and Parabolic Equations

By Jianghao Hao, Zhuangyi Liu, J. Yong. 2014

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In this paper, we provide a complete regularity analysis for an abstract system of coupled hyperbolic and parabolic equations in a complex Hilbert space. We are able to decompose the unit square of the parameters into three parts where the semigroup associated with the system is analytic, of specific order Gevrey classes, and non-smoothing, respectively. Moreover, we will show that the orders of Gevrey class are sharp, under proper conditions.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d0f3a9e0d81e422a30a3a8d309a262fbd3324e6e