Hairer's theory of regularity structures allows to interpret and solve a large class of SPDE from Mathematical Physics. A key structural assumption on these equations is that they are semi-linear (i.e. the leading term of the equation is linear and only lower order terms are non-linear), because this allows to rewrite the differential as an integral equation using Duhamel’s principle.

In this talk I will discuss how to extend the ideas underlying the theory of regularity structure to solve “more non-linear” equations, using the example

\partial_t u - a(u)\partial_x^2 = f

for a uniformly elliptic $a$ and for a rough driving noise $f$, e.g. space-time white noise.

This is joint work with F. Otto, J. Sauer and S. Smith (Leipzig).