Semidiscretizzazione di Galerkin di sistemi parabolico-ordinari semilineari
Received: 7 July 1998
Mathematics Subject Classification (2000): 35K57 - 65N30
Abstract: We consider a general system of n1 semilinear parabolic partial differential equations and n2 ordinary differential equations, with locally Lipschitz continuous nonlinearities. We analyse the well-posedness of this problem, exploiting the tools of the semigroups theory, and derive other further regularity results and conditions for the boundedness of the solution. We define the Galerkin semidiscrete approximation to the system and derive optimal order error estimates in L2 norm, under various assumptions on the nonlinear terms, on the finite dimensional subspaces in which the approximation is sought and on the regularity of the exact solution. As a further result, we provide maximum norm estimates for the approximation error and hence, by continuity arguments, we can conclude that the approximate solution is globally defined and bounded.