Strong Global Attractor for a Quasilinear Nonlocal Wave Equation on R
نویسندگان
چکیده
We study the long time behavior of solutions to the nonlocal quasilinear dissipative wave equation utt − φ(x)‖∇u(t)‖∆u+ δut + |u|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 )× Lg(R ).
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