Semigroup associated with a quasi-linear system in which the coupling is linear

Until now, semigroup solution has been successful mainly for linear and mildly nonlinear initial value problems having but a single partial differential equation (PDE). Attempts to apply standard semigroup generation principles to systems of nonlinear PDEs have encountered difficulties, though papers have appeared that treat mildly nonlinear systems. The purpose of this work is to demonstrate ideas, involving the Trotter product formula, that may be efficacious in finding semigroups for coupled systems of quasi-linear PDEs. This is a class for which semigroup generation principles involving accretiveness of an operator have generally failed. These Trotter product ideas were originally explained by J. Marsden, using a profound Banach manifold approach. 5 references