ABSTRACT
As a continuation of the previous chapter, this chapter deals with the initial-boundary value problems of weakly coupled semilinear parabolic systems. First, the L p theory, Schauder theory and Schauder fixed point theorem are used to investigate the local existence and uniqueness of solutions to initial-boundary value problems of weakly coupled nonlinear systems. Second, by applying the Schauder fixed point theorem it is proved that if a problem admits a pair of the coupled upper and lower solutions, then it must have a unique solution located between upper and lower solutions. Third, by means of coupled upper and lower solutions, we construct the monotone iterative sequences to obtain the unique solution. Examples are included to illustrate this method.
