Observability inequality for piecewise Hermite cubic orthogonal spline collocation semi‐discretization of the wave‐Petrovsky system with memory

Abstract

AbstractIn this paper we consider the piecewise Hermite cubic orthogonal spline collocation semi‐discretization of the wave‐Petrovsky coupled systems in the presence of memory terms. We treat the question of uniform observability for the semi‐discretization. We prove that an uniform observability inequality property in a subspace of solutions generated by filtering some frequencies holds true. The method of proof is Fourier series developments. The analysis is supported by numerical simulations.