ﻻ يوجد ملخص باللغة العربية
In this paper, we give a harmonic analysis proof of the Neumann boundary observability inequality for the wave equation in an arbitrary space dimension. Our proof is elementary in nature and gives a simple, explicit constant. We also extend the method to prove the observability inequality of a visco-elastic wave equation.
We give a direct analytic proof of the classical Boundary Harnack inequality for solutions to linear uniformly elliptic equations in either divergence or non-divergence form.
We investigate observability and Lipschitz stability for the Heisenberg heat equation on the rectangular domain $$Omega = (-1,1)timesmathbb{T}timesmathbb{T}$$ taking as observation regions slices of the form $omega=(a,b) times mathbb{T} times mathbb{
This paper is concerned with the existence and the regularity of global solutions to the linear wave equation associated with two-point type boundary conditions. We also investigate the decay properties of the global solutions to this problem by the construction of a suitable Lyapunov functional.
We solve the Cauchy problem for the $n$-dimensional wave equation using elementary properties of the Bessel functions.
We solve the Cauchy problem for the $n$-dimensional wave equation using elementary properties of the Fourier transform.