Asymptotic behavior of solutions of a time-space fractional diffusive Volterra equation
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913700795908096 |
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| author | Ahmad, Sofwah Kirane, Mokhtar |
| author_facet | Ahmad, Sofwah Kirane, Mokhtar |
| contents | In this paper, we study the time-space fractional differential equation of the Volterra type:
\begin{align*}
{D}^α_{0 \vert t} (u) +(-Δ_N)^σu &= u(1+au-bu^2)-au\int_0^t {K}(t-s) u(\cdot) \, ds,
\end{align*}
where $a,b>0$ are given constants, $α,σ\in (0,1)$, equipped with a homogeneous Neumann's boundary condition and a positive initial data. The boundedness and uniform continuity of the solution on the entire $\mathbb{R}^+$ are established. Moreover, the asymptotic behavior of the positive solution is investigated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14725 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic behavior of solutions of a time-space fractional diffusive Volterra equation Ahmad, Sofwah Kirane, Mokhtar Analysis of PDEs 26A33, 35B09, 35B40, 34K37, 35R09, 35R11 In this paper, we study the time-space fractional differential equation of the Volterra type: \begin{align*} {D}^α_{0 \vert t} (u) +(-Δ_N)^σu &= u(1+au-bu^2)-au\int_0^t {K}(t-s) u(\cdot) \, ds, \end{align*} where $a,b>0$ are given constants, $α,σ\in (0,1)$, equipped with a homogeneous Neumann's boundary condition and a positive initial data. The boundedness and uniform continuity of the solution on the entire $\mathbb{R}^+$ are established. Moreover, the asymptotic behavior of the positive solution is investigated. |
| title | Asymptotic behavior of solutions of a time-space fractional diffusive Volterra equation |
| topic | Analysis of PDEs 26A33, 35B09, 35B40, 34K37, 35R09, 35R11 |
| url | https://arxiv.org/abs/2502.14725 |