**SIMONA SANFELICI**

*Semidiscretizzazione di Galerkin di sistemi parabolico-ordinari semilineari*

**Pages:** 81-101

**Received:** 7 July 1998

**Mathematics Subject Classification (2000):** 35K57 - 65N30

**Abstract**:
We consider a general system of n_{1} semilinear
parabolic partial differential equations and n_{2} 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 L^{2}
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.

Home Riv.Mat.Univ.Parma