In this paper we consider the initial value problem for a plate type equation with variable coefficients and memory in ), which is of regularity-loss property. By using spectrally resolution, we study the pointwise estimates in the spectral space of the fundamental solution to the corresponding linear problem. Appealing to this pointwise estimates, we obtain the global existence and the decay estimates of solutions to the semilinear problem by employing the fixed point theorem.
Title = "Decay Property for Solutions to Plate Type Equations with Variable Coefficients",
Journal ="International Journal of Computer Applications Technology and Research(IJCATR)",
Volume = "7",
Pages ="241 - 291",
Year = "2018",
Authors ="Shikuan Mao, Xiaolu Li"}
The paper studies a type of equation with variable coefficient
Spectral resolution are used in the analysis
Regularity-loss property is measured by inhomogeneous Sobolev spaces
Similar decay estimates are obtained without L1-assumption on the initial data.