2017/06/20 by EL-Mennaoui, Omar, Laasri, Hafida
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1706.06895
This paper deals with the approximation of non-autonomous evolution equations of the form u(t)+A(t)u(t)=f(t) t∈[0,T], u(0)=u0. where A(t), t∈ [0,T] arise from a non-autonomous sesquilinear forms \mathfrak a(t;⋅,⋅) on a Hilbert space H with constant domain V⊂ H. Assuming the existence of a sequence \mathfrak an:[0,T]× V× V\longrightarrow\mathbb C, n∈ \mathbb N of non-autonomous forms such that the associated Cauchy problem has L2-maximal regularity in H and \mathfrak an(t,u,v) converges to \mathfrak a(t,u,v) as n→ ∞, then among others we show under additional assumptions that the limit problem has L2-maximal regularity. Further we show that the convergence is uniformly on the initial data u0 and the inhomogeneity f.