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.
Differential and Integral Equations
Lin, C., & Goldstein, J. (1993). Well-posedness and asymptotics of solutions for a class of wave equations with a nonlinear boundary stabilizer. Differential and Integral Equations, 6 (4), 899-904. Retrieved from https://digitalcommons.memphis.edu/facpubs/6127