Seminar Analysis and Mathematical Physics: Stefano Spirito (Università degli Studi dell'Aquila)

On the Kelvin-Voigt model for Viscoelastic material

I will review the existence and uniqueness theory of a model for viscoelastic materials of Kelvin-Voigt type with large strain. In particular, I will first review the existence theory in L2, and then show that also propagation of H1-regularity for the deformation gradient of weak solutions in two and three dimensions holds.  Moreover, in two dimensions it is also possible to prove uniqueness of weak solutions. Additional propagation of higher regularity can be obtained, leading to a global in time existence of smooth solutions. Joint work with K. Koumatos (U. of Sussex), C. Lattanzio (UnivAQ) and A. Tzavaras (KAUST).

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