Large-data solutions in one-dimensional thermoviscoelasticity involving temperature-dependent viscosities

2025/04/29 by Michael Winkler, Winkler, Michael · 1 citation
Engineering · Mathematics · #35D30 #35L05 #74F05 #74H20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2504.20480

openalex publication_date 2025/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An initial-boundary value problem for \ u_tt = (γ(Θ) u_xt)_x + au_xx - (f(Θ))_x, · amp; x∈Ω, t · gt;0,
Θ_t = Θ_xx + γ(Θ) u_xt² - f(Θ) u_xt, · amp; x∈Ω, t · gt;0, . is considered in an open bounded real interval Ω. Under the assumption that γ∈ C⁰([0,∞)) and f∈ C⁰([0,∞)) are such that f(0)=0, and k_γ≤ γ≤ K_γ as well as |f(ξ)| ≤ K_f ⋅ (ξ+1)^α for all ξ≥ 0 with some k_γ>0, K_γ>0, K_f>0 and α<(3)/(2), for all suitably regular initial data of arbitrary size a statement on global existence of a global weak solution is derived.

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• Existence, uniqueness, and time-asymptotics of regular solutions in multidimensional thermoelasticity on domains with boundary

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