Null controllability of linear heat and wave equations with nonlocal spatial terms

In this paper, we study the null controllability of linear heat and wave equations with spatial nonlocal integral terms. Under some analyticity assumptions on the corresponding kernel, we show that the equations are controllable. We employ compactness-uniqueness arguments in a suitable functional setting, an argument that is harder to apply for heat equations because of its very strong time irreversibility. Some possible extensions and open problems concerning other nonlocal systems are presented.Ministerio de Economía y CompetitividadNational Natural Science Foundation of ChinaMinisterio de Ciencia e InnovaciónEuropean Research Council Executive AgencyEuropean Office of Aerospace Research and DevelopmentAir Force Office of Scientific Researc