ABSTRACT
This chapter deals with hyperbolic partial differential equations relative to monotone iterates and fast convergence. Since the approaches utilized for elliptic and parabolic equations do not work for hyperbolic equations, we shall first proceed to consider, in Section 4.2, linear second-order hyperbolic problems and develop the variation of parameters formula using Laplace in variants. We then derive several comparison results of interest and consider also the important case of constant coefficients. In Section 4.3, we shall introduce suitable compact notation to reduce the complexity that is gen erated in the investigation of nonlinear hyperbolic IBVPs. We then address the extension of the monotone iterative technique in the general framework so that one can derive several special cases of interest. Section 4.4 is dedi cated to the method of generalized quasilinearization which complicates the process even further and necessitates the use of the compact notation of Section 4.3.
