Cari tutti, martedì prossimo (24 novembre) Alberto Bressan terrà un seminario al dipartimento di Matematica. Mi scuso fin d'ora per le altre copie di questo avviso che potreste ricevere.

Dear all, next Tuesday (November 24) Alberto Bressan will give a talk at the Mathematics Department. I apologize for the multiple copies of this message that you might receive.

Giovanni Alberti

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speaker: Alberto Bressan (Penn State University) title: Lipschitz Metrics for Nonlinear Wave Equations when: November 24, 2015, at 5 PM where: Dipartimento di Matematica, Sala Riunioni.

Abstract. The talk is concerned with some classes of nonlinear wave equations: of first order, such as the Camassa-Holm equation, or of second order, as the variational wave equation $u_{tt} − c(u) (c(u)u_x)_x=0$. In both cases, it is known that the equations determine a unique flow of conservative solutions within the natural "energy" space $H^1(R)$. However, this flow is not continuous w.r.t. the $H^1$ distance.

Our goal is to construct a new metric, which renders this flow uniformly Lipschitz continuous on bounded subsets of $H^1$. For this purpose, $H^1$ is given the structure of a Finsler manifold, where the norm of tangent vectors is defined in terms of an optimal transportation problem. For paths of piecewise smooth solutions, one can carefully estimate how the weighted length grows in time. To complete the construction, one needs an additional argument showing that the family of piecewise smooth solutions is dense. This generic regularity property can be proved using a variable transformation that reduces the equations to a semilinear system, followed by an application of Thom's transversality theorem.

link http://www.dm.unipi.it/webnew/it/seminari/lipschitz-metrics-nonlinear-wave-equations-0 to the seminar webpage at the Math Department

________________________________________________________ Prof. Giovanni ALBERTI Dipartimento di Matematica, Università di Pisa largo Pontecorvo 5 I-56127 Pisa ITALY

e-mail: galberti1@dm.unipi.it tel: +39 - 050 2213 239, fax: +39 - 050 2210 678 home page: http://www.dm.unipi.it/~alberti ________________________________________________________