On the right multiplicative perturbation of non-autonomous Lᵖ-maximal regularity

الأصل · EN

This paper is devoted to the study of Lᵖ-maximal regularity for non-autonomous linear evolution equations of the form equation*Multi-pert1-diss-non u(t)+A(t)B(t)u(t)=f(t)t∈[0,T],u(0)=u₀. equation* where {A(t),t∈ [0,T]} is a family of linear unbounded operators whereas the operators {B(t),t∈ [0,T]} are bounded and invertible. In the Hilbert space situation we consider operators A(t), t∈[0,T], which arise from sesquilinear forms. The obtained results are applied to parabolic linear differential equations in one spatial dimension.