401-5003-69L  Weak Convergence Methods for Nonlinear Partial Differential Equations

SemesterHerbstsemester 2019
DozierendeC. Evans
Periodizitäteinmalige Veranstaltung

KurzbeschreibungNachdiplom lecture
InhaltThis course will be an ambitious survey of rigorous methods for understanding solutions u^ε of various nonlinear PDE in various asymptotic limits. Assuming in particular that the u^ε converge weakly as ε → 0, we want to identify what PDE the weak limit u solves. This can be a hugely complicated problem, since the weak convergence is usually incompatible with the nonlinearities; but a rich variety of modern techniques can handle these issues for many interesting cases.

The lectures will discuss recent developments concerning (i) asymptotics for ODE, (ii) maximum principle methods, (iii) convexity and monotonicity, (iv) oscillations and compensated compactness, and (v) defect measures, with many examples and applications.