\(p\)-adic analogue of the wave equation. (English) Zbl 1473.35674
Summary: In this paper, a \(p\)-adic analogue of the wave equation with Lipschitz source is considered. Since it is hard to arrive the solution of the problem, we propose a regularized method to solve the problem from a modified \(p\)-adic integral equation. Moreover, we give an iterative scheme for numerical computation of the regularlized solution.
MSC:
| 35S10 | Initial value problems for PDEs with pseudodifferential operators |
| 30G06 | Non-Archimedean function theory |
| 35R11 | Fractional partial differential equations |
| 46S10 | Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis |
| 11D88 | \(p\)-adic and power series fields |
| 11S80 | Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.) |
| 12H25 | \(p\)-adic differential equations |
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