Mixed problems for the string vibration equation with nonlocal conditions of the general form at the right endpoint and with an inhomogeneous condition at the left endpoint
| Autor: | I. S. Mokrousov |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
0209 industrial biotechnology
Partial differential equation General Mathematics Weak solution 010102 general mathematics Mathematical analysis Recursion (computer science) 02 engineering and technology 01 natural sciences symbols.namesake 020901 industrial engineering & automation Ordinary differential equation Dirichlet boundary condition symbols Uniqueness Boundary value problem 0101 mathematics Linear combination Analysis Mathematics |
| Zdroj: | Differential Equations. 53:509-515 |
| ISSN: | 1608-3083 0012-2661 |
| Popis: | We consider four mixed problems for the string vibration equation with zero initial conditions, with a Bitsadze–Samarskii boundary condition of the general form at the right endpoint, and with an inhomogeneous Neumann or Dirichlet condition at the left endpoint. We prove the uniqueness of a generalized solution (in the sense of Il’in) of these problems and obtain an analytic representation of these solutions. The solution of each of the problems is represented in the form of a linear combination of functions constructed from the problem data, and recursion formulas for the coefficients of this linear combination are obtained. |
| Databáze: | OpenAIRE |
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