Existence, stability and smoothness of a bounded solution for nonlinear time-varying thermoelastic plate equations
Abstract:
In this paper we study the existence, stability and the smoothness of a bounded solution of the following nonlinear time-varying thermoelastic: plate equation with homogeneous Dirichlet boundary conditions utt + Δ2u + αΔθ = f1 (t, u, θ), t ≥, 0, x ∈ Ω, θt - βΔθ - αΔut = f2(t, u, θ), t ≥, 0, x ∈ Ω, θ = u = Δu = 0, t ≥ 0, x ∈ ∂Ω, where α ≠ 0, β > 0, Ω is a sufficiently regular bounded domain in ℝN (N ≥, 1) and f1e, f2e :ℝ × L2(Ω 2 → L2(Ω) define by fe(t, u, θ)(x) = f(t, u(x), θ(x)), x ∈ Ω, are continuous and locally Lipschitz functions. First, we prove that the linear system (f1 = f2 = 0) generates an analytic strongly continuous semigroup which decays exponentially to zero. Second, under some additional condition we prove that the nonlinear system has a bounded solution which is exponentially stable, and for a large class of functions f1, f2 this bounded solution is almost periodic. Finally, we use the analyticity of the semigroup generated by the linear system to prove the smoothness of the bounded solution. © 2003 Elsevier Inc. All rights reserved.
Año de publicación:
2003
Keywords:
- Smoothness
- Thermoelastic plate equation
- Exponential stability
- Bounded solutions
Fuente:
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Tipo de documento:
Article
Estado:
Acceso abierto
Áreas de conocimiento:
- Sistema no lineal
- Sistema no lineal
- Sistema no lineal
Áreas temáticas:
- Análisis