Wave equations with point interactions in finite energy spaces
نویسندگان
چکیده
منابع مشابه
Wave Equations with Point Interactions in Finite Energy Spaces
Given the abstract wave equation φ̈−∆αφ = 0, where ∆α is the Laplace operator with a point interaction of strength α, we define and study W̄α, the associated wave generator in the phase space of finite energy states. We prove the existence of the phase flow generated by W̄α, and describe its most relevant properties with particular emphasis on the associated symplectic structure and scattering the...
متن کاملFinite Speed of Propagation and Local Boundary Conditions for Wave Equations with Point Interactions
We show that the boundary conditions entering in the definition of the self-adjoint operator ∆ describing the Laplacian plus a finite number of point interactions are local if and only if the corresponding wave equation φ̈ = ∆φ has finite speed of propagation.
متن کاملFinite Energy Travelling Waves for Nonlinear Damped Wave Equations
E(u,ut) = f |Vu|2 + m\u\2 + |ut|2 dx — [ |u|"+1 dx, (1.3) 2 JRn a+ 1 JR„ which represents a Lyapunov function of the problem, i.e., it is decreasing along any nonstationary trajectory of (1.1). Employing the potential-well arguments of PAYNE-SATTINGER [16] one observes that any solution of (1.1) emanating from sufficiently small initial data exists globally for all t e R+ and tends to zero with...
متن کاملCoupled fixed point on ordered cone metric spaces with application in integral equations
Our theorems are on ordered cone metric spaces which are not necessarily normal. In the end, we describe the application of the main results in the integral equation.Although Du in [W. S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Analysis, 72(2010) 2259-2261.], showed that the fixed point results in the setting of cone...
متن کاملSolution of Wave Equations Near Seawalls by Finite Element Method
A 2D finite element model for the solution of wave equations is developed. The fluid is considered as incompressible and irrotational. This is a difficult mathematical problem to solve numerically as well as analytically because the condition of the dynamic boundary (Bernoulli’s equation) on the free surface is not fixed and varies with time. The finite element technique is applied to solve non...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2001
ISSN: 0022-2488
DOI: 10.1063/1.1360194