Problem for an Inhomogeneous Second-Order Evolutionary Equation with Homogeneous Integral Conditions
| Autor: | G. Kuduk, I. V. Kohut, Zinovii Nytrebych, P. I. Kalenyuk |
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| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Partial differential equation Applied Mathematics General Mathematics 010102 general mathematics Mathematical analysis Banach space Measure (physics) Riemann–Stieltjes integral Electric-field integral equation 01 natural sciences Integral equation 010101 applied mathematics Daniell integral 0101 mathematics Variable (mathematics) Mathematics |
| Zdroj: | Journal of Mathematical Sciences. 223:1-17 |
| ISSN: | 1573-8795 1072-3374 |
| DOI: | 10.1007/s10958-017-3334-3 |
| Popis: | We propose a method for the solution of the problem with homogeneous integral conditions for an inhomogeneous evolutionary equation with abstract operator in a Banach space H . The right-hand side of the evolutionary equation that belongs, for the fixed time variable, to a special subspace N ⊆ H can be represented as a Stieltjes integral with respect to a certain measure. The solution of this problem is also represented as a Stieltjes integral with respect to the same measure. We present examples of application of the method to the solution of the problem with integral conditions for the second-order partial differential equation in the time variable and, in general, an infinite-order partial differential equation in the space variable. |
| Databáze: | OpenAIRE |
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