Perturbation index of linear partial differential-algebraic equations

Abstract

For numerous problems in science and engineering a refined modeling approach leads to initial-boundary value problems for partial differential-algebraic equations (PDAEs). The paper investigates linear PDAEs from the point of view of weakly differentiable in space solutions. The appropriate treatment of boundary conditions is obtained by the requirement that the spatial differential operator has to satisfy a Gårding-type inequality in suitable function spaces. Based on this, an index concept extending the classical perturbation index is introduced.