2021/08/23 by Ming Wang, Can Zhang, Wang, Ming +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2108.09997
openalex publication_date 2021/08/23 · openalex created_date 2021/08/30 · openalex updated_date 2026/07/28
In this paper, we study quantitative spatial analytic bounds and unique continuation inequalities of solutions for fractional heat equations with an analytic lower order term on the whole space. At first, we show that the solution has a uniform positive analytic radius for all time, and the solution enjoys a log-type ultra-analytic bound if the coefficient is ultra-analytic. Second, we prove a Hölder type interpolation inequality on a thick set, with an explicit dependence on the analytic radius of coefficient. Finally, by the telescoping series method, we establish an observability inequality from a thick set. As a byproduct of the proof, we obtain observability inequalities in weighted spaces from a thick set for the classical heat equation with a lower order term.