We consider coupled parabolic systems with homogeneous boundary conditions. We establish a family of \(L^q\)-Carleman inequalities, \(q\in [2,\infty )\) and use them to obtain stability estimates in \(L^q\) and \(L^\infty \) norms for the sources in terms of the solution in a subdomain. We apply these estimates to reaction–diffusion systems.

中文翻译：

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非线性反应扩散系统逆源问题的稳定性

我们考虑具有齐次边界条件的耦合抛物线系统。我们建立了一系列\(L^q\) -Carleman 不等式\(q\in [2,\infty )\)并使用它们来获得\(L^q\)和\(L^\ ) 的稳定性估计infty \)就子域中的解决方案而言的源规范。我们将这些估计应用于反应扩散系统。