scholarly journals A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain

2020 ◽  
Vol 19 (12) ◽  
pp. 5387-5411
Author(s):  
Ahmad Z. Fino ◽  
◽  
Wenhui Chen ◽  
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Exterior Domain ◽  
Existence Result ◽  
Two Dimensional ◽  
Damped Wave Equation ◽  
Strongly Damped Wave Equation ◽  
Mixed Nonlinearity ◽  
Strongly Damped ◽  
Global Existence Result

Global Existence for the Two-Dimensional Euler Equations in a Critical Besov Space

2011 ◽  
Vol 271-273 ◽  
pp. 791-796
Author(s):  
Kun Qu ◽  
Yue Zhang
Keyword(s):  
Global Existence ◽  
Transport Equation ◽  
Besov Space ◽  
Euler Equations ◽  
Existence Result ◽  
Two Dimensional ◽  
Critical Besov Space ◽  
Global Existence Result

In this paper we prove the global existence for the two-dimensional Euler equations in the critical Besov space. Making use of a new estimate of transport equation and Littlewood-Paley theory, we get the global existence result.

scholarly journals Controllability of the Strongly Damped Wave Equation with Impulses and Delay

2017 ◽  
Vol 4 (1) ◽  
pp. 31-39
Author(s):  
Hugo Leiva
Keyword(s):  
Wave Equation ◽  
Distributed Control ◽  
Fixed Point Theorems ◽  
Nonempty Subset ◽  
Damped Wave Equation ◽  
Initial State ◽  
Final State ◽  
Strongly Damped Wave Equation ◽  
Approximately Controllable ◽  
Strongly Damped

AbstractEvading fixed point theorems we prove the interior approximate controllability of the following semilinear strongly damped wave equation with impulses and delay in the space Z1/2 = D((−Δ)1/2)×L2(Ω),where r > 0 is the delay, Γ = (0, τ)×Ω, ∂Γ = (0, τ) × ∂Ω, Γr = [−r, 0] × Ω, (ϕ,ψ) ∈ C([−r, 0]; Z1/2), k = 1, 2, . . . , p, Ω is a bounded domain in ℝℕ(ℕ ≥ 1), ω is an open nonempty subset of , 1 ω denotes the characteristic function of the set ω, the distributed control u ∈ L2(0, τ; U), with U = L2(Ω),η,γ, are positive numbers and f , Ik ∈ C([0, τ] × ℝ × ℝ; ℝ), k = 1, 2, 3, . . . , p. Under some conditions we prove the following statement: For all open nonempty subsets Ω of the system is approximately controllable on [0,τ]. Moreover, we exhibit a sequence of controls steering the nonlinear system from an initial state (ϕ (0), ψ(0)) to an ε-neighborhood of the final state z1 at time τ > 0.

Sign in / Sign up

Export Citation Format

Share Document