On the Unique Solvability of a Three-Point Problem for Partial Differential Equation in a Two-Dimensional Domain
| Autor: | Zinovii Nytrebych, Volodymyr Il'kiv, I. I. Volyans’ka, P. I. Kalenyuk |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Partial differential equation Plane (geometry) Applied Mathematics General Mathematics 010102 general mathematics 01 natural sciences Domain (mathematical analysis) 010305 fluids & plasmas Exponential function Periodic function Uniqueness theorem for Poisson's equation Hadamard transform 0103 physical sciences Applied mathematics 0101 mathematics Fourier series Mathematics |
| Zdroj: | Journal of Mathematical Sciences. 246:170-187 |
| ISSN: | 1573-8795 1072-3374 |
| DOI: | 10.1007/s10958-020-04728-x |
| Popis: | We study the problem with three-point conditions with respect to the time for a homogeneous partial differential equation in a plane domain. It is shown that the problem is well-posed in Hadamard's sense. This distinguishes the analyzed problem from the conditionally well-posed problem with many spatial variables whose solvability is connected with the problem of small denominators. The uniqueness theorem is proved and the conditions of existence of the solution of the problem with values in the spaces of periodic functions with exponential variation of the Fourier coefficients are established. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|