Nonlinear Evolution Equations with Infinitely Many Derivatives

We study the nonlinear evolutionary euclidean bosonic string ut=Δe-cΔu + U(t, u), c > 0 on the Euclidean space Rn. We interpret the nonlocal operator Δe-cΔ using entire vectors of Δ in L2(Rn). We prove that it generates a bounded holomorphic C0-semigroup on L2(Rn) (so that it also satisfies maximal Lp regularity) and we show the well-posedness of the corresponding nonlinear Cauchy problem. © 2016, Springer International Publishing.