Well-posedness and asymptotics of solutions for a class of wave equations with a nonlinear boundary stabilizer


Of concern is the following wave equation with nonlinear dissipation on the boundary: Utt(x, t) = Uxx(x, t) for (x, t) ∈ (0, l) X (0, ∞), ux(0, t) ∈,β0(ut(0, t)),-ux(l, t) ∈ (ut(l, t)), u(x, 0) = uo(x), ut(x, 0) = v0(x), where β0 and β1 are maximal monotone graphs in R X R each containing the origin. We prove the well-posedness and obtain the associated w-limit set. © 1993, Khayyam Publishing.

Publication Title

Differential and Integral Equations

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