Palestra: Controllability properties of anomalous diffusion phenomena
Palestrante: Sorin Micu (University of Craiova and Institute of Statistical Mathematics and Applied Mathematics, Romênia)
Resumo: Many physical phenomena are characterized by an anomalous diffusion when the mean square displacement of a particle will grow at a nonlinear rate in time. Some typical examples are the subdiffusional mobility of the proteic macromolecules in overcrowded cellular cytoplasm and the smoke's superdiffusion in turbulent atmosphere. We consider a simple one dimensional linear model which describes an anomalous diffusive behavior, involving a fractional Laplace operator, and we study its controllability property. If the fractional power of the Laplace operator is less or equal than 1/2 we are dealing with a subdiffusion phenomenon and the system is not spectrally controllable. The aim of the paper is twofold. Firstly, to analyze the possibility of controlling a finite number N of eigenmodes of the solution and to find the behavior of the corresponding controls when N tends to infinity. Secondly, to investigate the null-controllability property of the system when the support of the control moves linearly with respect to time.