On solvability of the dissipative Kirchhoff equation with nonlinear boundary damping

다국어 초록 (Multilingual Abstract)

In this paper, we prove the global existence and uniqueness of the dissipative Kirchhoff equation utt −M(∥∇u∥2)△u + αut + f(u) = 0 in Ω [0,∞), u(x, t) = 0 on Γ1 × [0,∞), αu/αu + g(ut) = 0 on Γ0 × [0,∞), u(x, 0) = u0, ut(x, 0) = u1 in Ω

with nonlinear boundary damping by Galerkin approximation benefited from the ideas of Zhang et al. [33]. Furthermore,we overcome some dif- ficulties due to the presence of nonlinear terms M(∥∇u∥2) and g(ut) by introducing a new variables and we can transform the boundary value problem into an equivalent one with zero initial data by argument of compacity and monotonicity.

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