Error Estimate for the Stationary Galerkin Method Applied to a Semilinear Parabolic Equation with Alternating Time Direction

Resumo

We prove the existence and uniqueness of a solution in the space W₂^2,1(Q) to the first boundary value problem for a semilinear parabolic equation in a cylindrical domain Q ⊆ Rⁿ⁺¹. We obtain an error estimate in the W₂^1,0(Q)-norm in terms of eigenvalues of the selfadjoint spectral problem for a second order elliptic equation. Bibliography: 5 titles.