From 2 November 2020, the autumn semester 2020 will take place online. Exceptions: Courses that can only be carried out with on-site presence.
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401-5003-69L  Weak Convergence Methods for Nonlinear Partial Differential Equations

SemesterAutumn Semester 2019
LecturersC. Evans
Periodicitynon-recurring course
Language of instructionEnglish

AbstractNachdiplom lecture
ContentThis 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.