Locally Lipschitz perturbations of bisemigroups
This paper studies a class of ill-posed semilinear systems in abstract Banach spaces. The main result establishes the existence and uniqueness of local dichotomous mild solutions for any sufficiently small time interval \([t_1,t_2]\). Moreover, it is shown that the uniform \(C^0\)-norm of local dichotomous mild solutions depends continuously on \([t_1, t_2]\). It is also provided a simple example of a semilinear elliptic system that arises when considering solitary waves in an infinite cylinder. The proofs rely on standard arguments in the theory of nonlinear equations with infinitesimal generators in Banach spaces.
scientific article; zbMATH DE number 5711079