Abstract We consider systems of parabolic equations coupled in zero and first order terms. We establish Lipschitz estimates in L q {L^{q}} -norms, 2 ≤ q ≤ ∞ {2\leq q\leq\infty} , for the source in terms of the solution in a subdomain. The main tool is a family of appropriate Carleman estimates with general weights, in Lebesgue spaces, for nonhomogeneous parabolic systems.

中文翻译：

---

逆源抛物线问题的𝐿𝑞-范数的稳定性

摘要 我们考虑在零阶和一阶项中耦合的抛物线方程组。我们在 L q {L^{q}} -norms, 2 ≤ q ≤ ∞ {2\leq q\leq\infty} 中建立 Lipschitz 估计，对于子域中的解的源。主要工具是一系列适当的 Carleman 估计值，在 Lebesgue 空间中，用于非齐次抛物线系统的一般权重。