Well-posedness, smoothness, decay and propagation of singularities for evolution pdes with polynomially bounded coefficients
Välkommen till föreläsningen i seminarieserien i matematik.
I will give a survey about existing results and future challenges about the evolution pdes with variable coefficients admitting polynomial bounds, of hyperbolic and Schrödinger types. These classes of pdes have attracted a considerable attention by many authors along the past three decades, both in the deterministic case, as well as, in more recent times, in the stochastic case. I will focus on hyperbolic and Schrödinger type pdes on R^d in the above class. If time allows, I will also briefly discuss the extension of the analysis to analogous problems on asymptotically Euclidean manifolds.