反应-扩散-对流系统中时变系数的稳定确定
Stable determination of time-dependent coefficients in a reaction-diffusion-convection system
浏览论文内容
中文总结 AI 辅助
本文针对R^{1+n}（n≥2）有界域内反应-扩散-对流系统的逆边值问题，结合Carleman估计与几何光学解，通过部分边界测量得到时变对流系数的双对数稳定性估计，进而得到矩阵值势的三对数稳定性估计。
中文摘要 AI 辅助
本文研究R^{1+n}（n≥2）有界域内反应-扩散-对流系统的逆边值问题，旨在通过Dirichlet-to-Neumann映射表示的边界测量获取确定时变对流系数与矩阵值势的稳定性估计。考虑测量仅在侧边界略超一半子集上可用的部分数据情形，先建立相关初边值问题的适定性，再结合Carleman估计与合适的几何光学解推导未知系数的稳定性估计，具体证明从部分Dirichlet-to-Neumann映射知识得到时变对流系数的双对数（log-log）稳定性估计，该结果用于恢复矩阵值势，进而得到零阶系数的三对数（log-log-log）稳定性估计。
英文摘要
In this manuscript, we investigate an inverse boundary value problem for a reaction-diffusion-convection system in a bounded domain of $\mathbb{R}^{1+n}$, $n\geq 2$. We aim to obtain a stability estimate for determining the time-dependent convection coefficient and matrix-valued potential from boundary measurements represented by the Dirichlet-to-Neumann map. We consider a partial data setting in which the measurements are available only on a subset of the lateral boundary that slightly exceeds one-half of the boundary. We first establish the well-posedness of the associated initial-boundary value problem. Subsequently, by combining Carleman estimates with suitable geometric optics solutions, we derive stability estimates for the unknown coefficients. More precisely, we prove a double logarithmic ($\log$-$\log$) stability estimate for the time-dependent convection coefficient from the knowledge of the partial Dirichlet-to-Neumann map. This stability result is then employed to recover the matrix-valued potential, yielding a triple logarithmic ($\log$-$\log$-$\log$) stability estimate for the zeroth-order coefficient.
