We prove null controllability for linear and semilinear heat equations with dynamic boundary conditions of surface diffusion type. The results are based on a new Carleman estimate for this type of boundary conditions.2000 Mathematics Subject Classification. Primary: 93B05. Secondary: 35K20, 93B07. Key words and phrases. Parabolic problems, dynamic boundary conditions, surface diffusion, Carleman estimate, null controllability, observability estimate.We thank the Deutsche Forschungsgemeinschaft which supported this research within the grants ME 3848/1-1 and SCHN 570/4-1. M.M. thanks L.M. for a very pleasant stay in Marrakesh, where parts of this work originated.
In this paper we prove some new fixed point theorems in r-normed and locally r-convex spaces. Our conclusions generalize many well-known results and provide a partial affirmative answer to Schauder's conjecture. Based on the obtained results, we prove the analogue of a Von Neumann's theorem in locally r-convex spaces. In addition, an application to game theory is presented.
The aim of this paper is to study the wellposedness and L 2 -regularity, firstly for a linear heat equation with dynamic boundary conditions by using the approach of sesquilinear forms, and secondly for its backward adjoint equation using the Galerkin approximation and the extension semigroup to a negative Sobolev space.2010 Mathematics Subject Classification. 35A15; 35K20; 47D06.
In this paper, we characterize the stabilization of some delay systems. The proof of the main result uses the method introduced in Ammari and Tucsnak (ESAIM COCV 6:361-386, 2001) where the exponential stability for the closed loop problem is reduced to an observability estimate for the corresponding uncontrolled system combined with a boundedness property of the transfer function of the associated open loop system.
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