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$% L. A. Medeiros and M. Milla Miranda, On a nonlinear wave equation with damping, Rev. Mat. Univ. Complut. Madrid 3 (1990), no. 2, 3, 213–231.%$

On a Nonlinear Wave Equation with Damping

Luiz A. MEDEIROS and Manuel MILLA MIRANDA
Istituto de Matemática, UFRJ
Cx. Postal 68530 - CEP: 21944
Rio de Janeiro, RJ — Brazil

Received: October 10, 1989
 Revised: March 23, 1990
Dedicated to Jacques Louis Lions
on the occasion of his 60th birthday
ABSTRACT

In this work the authors prove the existence of global solutions for damping nonlinear wave equation * 1/2 2 * ' u + M( |A u|)Au+ A u = f , 0< a <1 . Uniqueness is obtained for 1/2 <a < 1 . They also prove the exponential decay for the energy, when 0 < a< 1 .

1980 Mathematics Subject Classification (1985 revision): 35L05.