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
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