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.

Pre-contoured reconstruction plate fabricated via three-dimensional printed bending support

“…Unfortunately, these plates often need to be removed due to plate exposure, screw loosening, fracture, or infection [1][2][3][4][5] . Failure of the plates is related to the size and location of the defect, smoking, diabetes, and pre-and postoperative radiation 1,[6][7][8][9] . Among these factors, plate exposure through the skin occurs in 3.8% to 46% of cases [6][7][8]10,11 .…”

“…Failure of the plates is related to the size and location of the defect, smoking, diabetes, and pre-and postoperative radiation 1,[6][7][8][9] . Among these factors, plate exposure through the skin occurs in 3.8% to 46% of cases [6][7][8]10,11 . Once the plates are exposed, the plates are removed and the wound repaired with a vascularized bone flap 11 .…”