论文标题
逆双曲热传导问题的变异准可逆性方法的收敛分析
Convergence analysis of a variational quasi-reversibility approach for an inverse hyperbolic heat conduction problem
论文作者
论文摘要
我们根据麦克斯韦（Maxwell-Cattaneo）模型的非感染热定律研究了时间转移的双曲热传导问题。这种热量和质量扩散问题是具有热记忆或有限的时间延迟热通量的热力学系统的双曲线类型方程，在该系统中，傅立叶或给范围的法律被证明与实验数据失败了。在这项工作中，我们表明，我们最近针对经典时间转移的热传导问题（遵守傅立叶或给法律法）的变异准可逆性方法可以适应这种双曲线场景。我们建立了一个通用正则方案，从某种意义上说，我们将两个涉及PDE的空间操作员扰动。在Carleman重量函数的驱动下，我们利用了自然能法来证明这种正规化方案的适当性。此外，我们证明了混合$ l^2 $ - $ h^1 $空间中的Hölder收敛速度。
We study a time-reversed hyperbolic heat conduction problem based upon the Maxwell--Cattaneo model of non-Fourier heat law. This heat and mass diffusion problem is a hyperbolic type equation for thermodynamics systems with thermal memory or with finite time-delayed heat flux, where the Fourier or Fick law is proven to be unsuccessful with experimental data. In this work, we show that our recent variational quasi-reversibility method for the classical time-reversed heat conduction problem, which obeys the Fourier or Fick law, can be adapted to cope with this hyperbolic scenario. We establish a generic regularization scheme in the sense that we perturb both spatial operators involved in the PDE. Driven by a Carleman weight function, we exploit the natural energy method to prove the well-posedness of this regularized scheme. Moreover, we prove the Hölder rate of convergence in the mixed $L^2$--$H^1$ spaces.
