Decay properties for evolution-parabolic coupled systems related to thermoelastic plate equations

Abstract

In this paper, we consider the Cauchy problem for a family of evolution-parabolic coupled systems, which are related to the classical thermoelastic plate equations containing non-local operators. By using diagonalization procedure and WKB analysis, we derive representation of solutions in the phase space. Then, sharp decay properties in a framework of $ L^p-L^q $ are investigated via these representations. Particularly, some thresholds for the regularity-loss type decay properties are found.

Keywords

• thermoelastic plate equations
• non-local operator
• decay properties
• regularity-loss
• wentzel-kramers-brillouin (wkb) analysis
• fractional power operators