Regularity Analysis for Two Coupled Second Order Evolution Equations

2025/08/28 by Chenxi Deng, Zhaobin Kuang, Deng, Chenxi +5
Engineering · Mathematics · #35B65 #35K90 #35L90 #47D03 #93D05 #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods for differential equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2508.20624

openalex publication_date 2025/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the regularity of the strongly continuous semigroup associated with a system of two coupled second order evolution equations with indirect damping, whose stability was recently studied by Hao et al. By deriving the asymptotic expression of the eigenvalues the generator, we partition the parameter space into several disjoint regions, where the semigroup exhibits either analyticity or Gevrey class regularity. Together with the estimate of the resolvent of the generator on the imaginary axis, we give a complete and sharp regularity characterization for this system.

Citations

• Regularity and stability of the semigroup associated with some interacting elastic systems I: A degenerate damping case
• Regularity Analysis for an Abstract System of Coupled Hyperbolic and Parabolic Equations
• Optimal polynomial decay of functions and operator semigroups

Related

• Regularity and stability of the semigroup associated with some interacting elastic systems I: A degenerate damping case
• Regularity Analysis for an Abstract System of Coupled Hyperbolic and Parabolic Equations
• Regularity of the semigroups associated with some damped coupled elastic systems II: a nondegenerate fractional damping case
• Second order linear evolution equations with general dissipation
• On the regularity of global attractors