Local and global existence of solutions to a strongly damped wave equation of the p-Laplacian type

2017/05/18 by Nicholas J. Kass, Kass, Nicholas J., Mohammad A. Rammaha +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1705.06696

openalex publication_date 2017/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article focuses on a quasilinear wave equation of p-Laplacian type: u_tt - Δ_p u - Δu_t=0 in a bounded domain Ω⊂ℝ³ with a sufficiently smooth boundary Γ=∂Ω subject to a generalized Robin boundary condition featuring boundary damping and a nonlinear source term. The operator Δ_p, 2 < p < 3, denotes the classical p-Laplacian. The nonlinear boundary term f (u) is a source feedback that is allowed to have a supercritical exponent, in the sense that the associated Nemytskii operator is not locally Lipschitz from W^1,p(Ω) into L²(Γ). Under suitable assumptions on the parameters we provide a rigorous proof of existence of a local weak solution which can be extended globally in time provided the source term satisfies an appropriate growth condition.

Citations

• Existence and Asymptotic Behavior for a Strongly Damped Nonlinear Wave Equation

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