论文标题
$ l_p $ - $ l_q $ - quasilinear非等温westervelt方程的理论
$L_p$-$L_q$-theory for a quasilinear non-isothermal Westervelt equation
论文作者
论文摘要
我们研究了一个由dirichlet或neumann边界条件的非线性声学和Pennes生物学方程组成的Quasilerear系统。 $ l_p $ - $ l_q $的最大规律性的概念用于证明本地和全球范围的良好性。此外，我们通过一个参数技巧显示了解决方案即时正规化的。最后，我们计算系统的平衡，并研究解决方案的长期行为，从均衡开始。
We investigate a quasilinear system consisting of the Westervelt equation from nonlinear acoustics and Pennes bioheat equation, subject to Dirichlet or Neumann boundary conditions. The concept of maximal regularity of type $L_p$-$L_q$ is applied to prove local and global well-posedness. Moreover, we show by a parameter trick that the solutions regularize instantaneously. Finally, we compute the equilibria of the system and investigate the long-time behaviour of solutions starting close to equilibria.
