Global solvability of Moore–Gibson–Thompson equation with memory arising in nonlinear acoustics
Global solvability of Moore–Gibson–Thompson equation with memory arising in nonlinear acoustics
复制标题
DOI：
10.1007/s00028-016-0353-3
复制
发表时间：
2017-03
影响因子：
1.4
通讯作者：
I. Lasiecka
中科院分区：
文献类型：
--
作者：
I. Lasiecka
考虑了一个三阶非线性时间方程。这种特殊的模型是由高频超声技术，占热和分子松弛的动机。由此产生的方程产生了具有潜在退化阻尼的准线性演化（Kaltenbacher in Evol Eqs Control Theory 4（4）：447-491，2015）。研究了光滑解的局部和全局（在时间上）存在性.本文的主要结果指出，适当的校准的内存内核，解决方案存在全球足够小，经常的初始数据。随着指数衰减的松弛核，所述解决方案表现出指数衰减率。该证明依赖于应用于一系列更高能量估计的“屏障”方法，沿着抽象表示和Pruss开发的粘弹演化理论（Arch Math 92：158-173，2009，Evolutionary integral equations and applications. Birkhauser，2012年）。
A third-order in time nonlinear equation with memory term is considered. This particular model is motivated by high-frequency ultrasound technology which accounts for thermal and molecular relaxation. The resulting equations give rise to a quasilinear-like evolution with a potentially degenerate damping (Kaltenbacher in Evol Eqs Control Theory 4(4):447–491, 2015). Local and global (in time) existence of smooth solutions is studied. The main result of the paper states that with appropriate calibration of the memory kernel, solutions exist globally for sufficiently small and regular initial data. With exponentially decaying relaxation kernel said solutions exhibit exponential decay rates. The proof relies on the “barrier” method applied to a string of higher energy estimates, along with an abstract representation and the theory of viscoleastic evolutions developed in Pruss (Arch Math 92:158–173, 2009, Evolutionary integral equations and applications. Birkhauser, 2012).