Back to Search
Start Over
Initial-Boundary Value Problem for the Beam Vibration Equation in the Multidimensional Case
- Source :
- Differential Equations. 55:1336-1348
- Publication Year :
- 2019
- Publisher :
- Pleiades Publishing Ltd, 2019.
-
Abstract
- In the multidimensional case, we study the problem with initial and boundary conditions for the equation of vibrations of a beam with one end clamped and the other hinged. An existence and uniqueness theorem is proved for the posed problem in Sobolev classes. A solution of the problem under consideration is constructed as the sum of a series in the system of eigenfunctions of a multidimensional spectral problem for which the eigenvalues are determined as the roots of a transcendental equation and the system of eigenfunctions is constructed. It is shown that this system of eigenfunctions is complete and forms a Riesz basis in Sobolev spaces. Based on the completeness of the system of eigenfunctions, a theorem about the uniqueness of a solution to the posed initial-boundary value problem is stated.
- Subjects :
- 0209 industrial biotechnology
Partial differential equation
Picard–Lindelöf theorem
Transcendental equation
General Mathematics
010102 general mathematics
Mathematical analysis
02 engineering and technology
Mathematics::Spectral Theory
01 natural sciences
Sobolev space
020901 industrial engineering & automation
Ordinary differential equation
Uniqueness
Boundary value problem
0101 mathematics
Analysis
Eigenvalues and eigenvectors
Mathematics
Subjects
Details
- ISSN :
- 16083083 and 00122661
- Volume :
- 55
- Database :
- OpenAIRE
- Journal :
- Differential Equations
- Accession number :
- edsair.doi...........55a699e3dd79e583e29277229ce21b71