WebThis paper is concerned with the exact boundary controllability for a degenerate and singular wave equation in a bounded interval with a moving endpoint. By the multiplier method and using an adapted Hardy-poincaré inequality, we prove direct and inverse inequalities for the solutions of the associated adjoint equation. As a consequence, by … WebAbstract. We study a wave equation in one space dimension with a general diffusion coefficient which degenerates on part of the boundary. Degeneracy is measured by a real parameter μ a > 0. We establish observability inequalities for weakly (when μ a ∈ [ 0, 1 [) as well as strongly (when μ a ∈ [ 1, 2 [) degenerate equations.
Asymptotic stability and blow-up for the wave equation with …
WebJun 14, 2024 · Use MathJax to format equations. MathJax reference. To learn more, see our tips on writing great answers. Sign up or log in. Sign up using Google Sign up using … Websystem (P) into an augmented system by coupling the degenerate wave equation with a suitable di usion equation and we show the well-posedness of our problem by semigroup theory. In section 3, we prove lack of exponential stability by spectral analysis and by using Bessel functions. In the last section, we prove an optimal decay rate. tri cities washington shooting
Physics Free Full-Text Cylindrical and Spherical Nucleus-Acoustic ...
WebKeywords: degenerate wave equation, drift, stabilization, exponential decay MSC: 35L80, 93D23, 93D15 ∗ The author is a member of the Gruppo Nazionale per l’Analisi Matematica, la Proba- This section intends to illustrate the existence of degenerate energy levels in quantum systems studied in different dimensions. The study of one and two-dimensional systems aids the conceptual understanding of more complex systems. In several cases, analytic results can be obtained more easily in the study of one-dimensional systems. For a quantum particle with a wave function moving in a one-dimensional potential , the t… WebOct 10, 2024 · The measurement has determined that we are either in state α 1 or α 2, but not which. Thus there is a partial collapse of the wavefunction onto a linear combination … tri cities washington television providers