Stability in 𝐿𝑞-norm for inverse source parabolic problems.

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. [ABSTRACT FROM AUTHOR]