Gradient flow equations of non convex functionals

seminar: Long time behaviour or a dynamical system related to the Perona Malik equation

speaker: Renato Colucci (Università de L'Aquila)

abstract: The asymptotic behaviour of a dissipative system can analyzed by means of the existence of a complicated attractor toward which orbits converge as $t \to +\infty$.Also in the case of infinite dimensional dynamical systems, it may happen that the degrees of freedom can be finite. Concerning the Perona Malik equation, we consider the problem of existence of absorbing sets, the existence and regularity of the global attractor for which we give an estimate of the dimension. Finally, we study the inertial manifold of the system, which turns out to be a Lipschitz manifold of finite dimension which exponentially attracts all orbits, it is positively invariant and contains the global attractor.

timetable:
Mon 2 May, 10:30 - 11:30, Sala Conferenze Centro De Giorgi
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