论文标题
在耗散情况下，Moore-Gibson-Thompson方程的Cauchy问题
The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case
论文作者
论文摘要
在本文中，我们研究了耗散案例中线性和半线性摩尔·吉布森 - 汤普森（MGT）方程的库奇问题。关于线性MGT模型，通过利用与傅立叶分析相关的WKB分析，我们得出了一些$ l^2 $估计的解决方案，从而改善了先前研究中的解决方案[46]。此外，在加权$ l^1 $空间的框架中，解决方案的渐近概况和近似关系。接下来，借助古典能量法和Hardy的不平等，我们获得了能量和解决方案本身的单一极限结果。关于半连接的MGT模型，基于这些尖锐的$ l^2 $估计并构建时间加权的Sobolev空间，我们研究了具有不同规律性的Sobolev Solutions的全球（及时）存在。最后，在初始数据的符号假设下，通过应用测试功能方法证明了全局（及时）弱解决方案的不存在。
In this paper, we study the Cauchy problem for the linear and semilinear Moore-Gibson-Thompson (MGT) equation in the dissipative case. Concerning the linear MGT model, by utilizing WKB analysis associated with Fourier analysis, we derive some $L^2$ estimates of solutions, which improve those in the previous research [46]. Furthermore, asymptotic profiles of the solution and an approximate relation in a framework of the weighted $L^1$ space are derived. Next, with the aid of the classical energy method and Hardy's inequality, we get singular limit results for an energy and the solution itself. Concerning the semilinear MGT model, basing on these sharp $L^2$ estimates and constructing time-weighted Sobolev spaces, we investigate global (in time) existence of Sobolev solutions with different regularities. Finally, under a sign assumption on initial data, nonexistence of global (in time) weak solutions is proved by applying a test function method.
