Full paper in PDF:
$%M. M. Cavalcanti, V. N. Domingos Cavalcanti, J. A. Soriano, and J. S. Prates Filho, Existence and asymptotic behavior for a degenerate Kirchhoff-Carrier model with viscosity and nonlinear boundary conditions, Rev. Mat. Complut. 14 (2001), no. 1, 177–203.%$

Existence and Asymptotic Behavior for a Degenerate Kirchhoff-Carrier Model with Viscosity and Nonlinear Boundary Conditions
Marcelo M. CAVALCANTI, Valéria N. DOMINGOS CAVALCANTI,
Juan A. SORIANO, and Júlio S. PRATES FILHO
Departamento de Matemática
Universidade Estadual de Maringá
87020-900 Maringá — PR, Brasil

Received: October 26, 1999
Accepted: August 3, 2000

ABSTRACT

The present paper studies the existence and uniqueness of global solutions and decay rates to the nonlinear hyperbolic problem

i ntegral @2y- M( | \~/ y|2dx)Dy--@Dy = 0 in Q = _O_ ×(0, oo ) @t2 _O_ @t { y = 0 on S1 = G1× (0, oo ) (*) ( integral 2 )@y- @-(@y) ||||g M _O_| \~/ y|dx @n + @t @n + |y| y = 0 on S0 = G0× (0, oo ) 0 @y 1 y(0)= y , @t(0) = y in _O_.

where M is a C1 function, M(c) > 0, A c > 0.

2000 Mathematics Subject Classification: 35B40, 35L80.