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 Some quasilinear hyperbolic equations and Yosida approximations Bull. Korean Math. Soc. 2001 Vol. 38, No. 3, 505-516 Jong Yeoul Park, Il Hyo Jung, and Yong Han Kang Pusan National University, Pusan National University, Pusan National University Abstract : We show the existence and uniqueness of solutions for the Cauchy problem for nonlinear evolution equations with the strong damping: $$u''(t) - M(|\nabla u(t)|^2) \triangle u(t) - \delta \triangle u'(t) = f(t).$$ As an application, a Kirchhoff model with viscosity is given. Keywords : Kirchhoff model, Yosida approximations, quasilinear hyperbolic equations MSC numbers : 35A05, 35L70 Downloads: Full-text PDF