Compactness for evolution problems in Banach spaces
par
Anastasiia Hraivoronska
→
Europe/Paris
Description
I will present two results on compactness that are motivated by applications to existence and asymptotic limit problems for evolutionary equations in Banach spaces, following the paper by Rossi and Savaré (http://www.numdam.org/article/ASNSP_2003_5_2_2_395_0.pdf). I will briefly review the compactness criteria by Aubin-Lions and Simon and present the unifying perspective on compactness in $L^p((0,T); B)$ by Rossi-Savaré. The approach employs general principles of "tightness" and "integral equicontinuity" and relies on methods from Young measure theory. I will show the necessary and sufficient condition for compactness in $L^p((0,T); B)$ and the related result on compactness with respect to convergence in measure.