Leaf Peeling method for the wave equation on metric tree graphs

نویسندگان

چکیده

We consider the dynamical inverse problem for wave equation on a metric tree graph and describe Leaf Peeling (LP) method. The main step of method is recalculating response operator from original to peeled tree. LP allows us recover connectivity, potential function lengths its edges given finite time interval.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Symmetries, Conservation Laws, and Wave Equation on the Milne Metric

Noether symmetries provide conservation laws that are admitted by Lagrangians representing physical systems. For partial differential equation possessing Lagrangians these symmetries are obtained by the invariance of the corresponding action integral. In this paper we provide a systematic procedure for determiningNoether symmetries and conserved vectors for a Lagrangian constructed from a Loren...

متن کامل

Schrodinger equation and wave equation on finite graphs

Abstract. In this paper, we study the schrodinger equation and wave equation with the Dirichlet boundary condition on a connected finite graph. The explicit expressions for solutions are given and the energy conservations are derived. Applications to the corresponding nonlinear problems are indicated. Mathematics Subject Classification 2000: 53Cxx,35Jxx

متن کامل

Blow up for the Semilinear Wave Equation in Schwarzschild Metric

We study the semilinear wave equation in Schwarzschild metric (3 + 1 dimensional space time). First, we establish that the problem is locally well posed in H for any σ > 1; then we prove the blow up of the solution for every p > 1 and non negative initial data. The work is dedicated to prof. Yvonne Choquet Bruhat in occasion of her 80th year.

متن کامل

On Inverse Dynamical and Spectral Problems for the Wave and Schrödinger Equations on Finite Trees. the Leaf Peeling

Interest in inverse dynamical, spectral and scattering problems for differential equations on graphs is motivated by possible applications to nano-electronics and quantum waveguides and by a variety of other classical and quantum applications. Recently a new effective leaf peeling method has been proposed by S. Avdonin and P. Kurasov [3] for solving inverse problems on trees (graphs without cyc...

متن کامل

Metric Dimension of Bounded Tree-length Graphs

The notion of resolving sets in a graph was introduced by Slater (1975) and Harary and Melter (1976) as a way of uniquely identifying every vertex in a graph. A set of vertices in a graph is a resolving set if for any pair of vertices x and y there is a vertex in the set which has distinct distances to x and y. A smallest resolving set in a graph is called a metric basis and its size, the metri...

متن کامل

ذخیره 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: Inverse Problems and Imaging

سال: 2021

ISSN: ['1930-8345', '1930-8337']

DOI: https://doi.org/10.3934/ipi.2020060