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

2023/09/21 by Paulo M. de Carvalho-Neto, de Carvalho-Neto, Paulo M., C.L. Frota +3 · 1 citation
Computer Science · Engineering · Mathematics · #26A33 #34A08 #35L05 #35R11 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2309.12453

openalex publication_date 2023/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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⊂ ℝⁿ, n ≥ 2, which includes simply connected regions. The boundary of Ω is made up of two disjoint pieces Γ₀ and Γ₁. Homogeneous Dirichlet conditions are enforced on Γ₀, while acoustic boundary conditions are considered on Γ₁. 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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