We show how to generalize Lyons’ rough paths theory in order to give a pathwise meaning to some non-linear infinite-dimensional evolution equations associated to an analytic semigroup and driven by an irregular noise. As an illustration, we apply the theory to a class of 1d SPDEs driven by a space-time fractional Brownian motion.

where the constant a is non-zero. However, (1.1) can be reduced to the standard evolution equation (3.4) in an appropriate space because the operator I − a∂2 x which acts on ∂tu(x, t) can be inverted. Thus, (1.1) is an example of a regular equation; we study such problems in Section 2. Section 3 is concerned with those regular equations of a special form suggested by (1.1). Another example whic...

In the spirit of the recent work of Ibragimov [1] who adopted the infinitesimal method for calculating invariants of families of differential equations using the equivalence groups, we apply the method to evolution type equations of the form ut = f(x, u)uxx + g(x, u, ux). We show that the equivalence Lie algebra admitted by this equation has two functionally independent differential invariants ...