Strong global attractor for a quasilinear nonlocal wave equation on ℝN
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We study the long time behavior of solutions to the nonlocal quasilinear dissipative wave equation
utt - ϕ(x) ∥∇u(t)∥2 ∆u + δut + |u|α u = 0,
in ℝN, t ≥ 0, with initial conditions u(x, 0) = u0(x) and ut(x, 0) = u1(x). We consider the case N ≥ 3, δ > 0, and (ϕ(x))-1 a positive function in LN/2(ℝN) ∩ L∞(ℝN). The existence of a global attractor is proved in the strong topology of the space D1,2(ℝN) x L2g(ℝN).
CitationPapadopoulos, P. G., & Stavrakakis, N. M. (2006). Strong global attractor for a quasilinear nonlocal wave equation on ℝN. Electronic Journal of Differential Equations, 2006(77), pp. 1-10.
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