Approximation of abstract Cauchy problems for dissipative operators with respect to metric-like functionals

摘要

This paper discusses approximation of semigroups of locally Lipschitz operators by discrete semigroups of local quasi-contractions with respect to metric-like functionals. The main approximation result not only extends a product formula for contractive semigroups generated by maximal dissipative operators in real Hilbert spaces but also gives an algorithm for solving a mixed problem for the Kirchhoff equation to which the contractive semigroup theory or Kato's quasilinear theory cannot directly apply. (C) 2019 Elsevier Inc. All rights reserved.