TY  - JOUR
ID  - Nakao2014
LB  - Nakao2014
AU  - Nakao, Mitsuhiro
TI  - Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity
ST  - Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2014
VL  - 34
IS  - 3
SP  - 569
EP  - 590
DO  - http://dx.doi.org/10.7494/OpMath.2014.34.3.569
UR  - http://dx.doi.org/10.7494/OpMath.2014.34.3.569
AB  - We prove the existence and uniqueness of a global decaying solution to the initial boundary value problem for the quasilinear wave equation with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a 'loan' method and use a difference inequality on the energy.
KW  - global solutions
KW  - energy decay
KW  - quasilinear wave equation
KW  - Kelvin-Voigt dissipation
KW  - derivative nonlinearity
SN  - 1232-9274
ER  -