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arXiv · 2309.12453

On the Initial Boundary Value Problem to the Time-Fractional Wave Equation with Acoustic Boundary Conditions

Paulo M. de Carvalho-Neto·Cícero L. Frota·Pedro G. P. Torelli
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Abstract

This paper is concerned with the study of the well-posedeness for the initial boundary value problem to the time-fractional wave equation with acoustic boundary conditions. The problem is considered in a bounded and connected domain $Ω\subset {\mathbb{R}^{n}}$, $n \geq 2$, which includes simply connected regions. The boundary of $Ω$ is made up of two disjoint pieces $Γ_{0}$ and $Γ_{1}.$ Homogeneous Dirichlet conditions are enforced on $Γ_0$, while acoustic boundary conditions are considered on $Γ_1$. To establish our main result, we employ the Faedo-Galerkin method and successfully solve a general system of time-fractional ordinary differential equations which extends the scope of the classical Picard-Lindelöf theorem.

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Paulo M. de Carvalho-Neto, Cícero L. Frota, Pedro G. P. Torelli. 2023-09-21. On the Initial Boundary Value Problem to the Time-Fractional Wave Equation with Acoustic Boundary Conditions. https://arxiv.org/abs/2309.12453

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