Global Existence and Asymptotic Behavior of Solutions for Some Nonlinear Hyperbolic Equation.

Authors :: Yaojun Ye
Source :: Journal of Inequalities & Applications; 2010, Vol. 2010, p1-10, 10p
Publication Year :: 2010
Abstract: The initial boundary value problem for a class of hyperbolic equation with nonlinear dissipative term u<subscript>tt</subscript> - Σ<superscript>n</superscript><subscript>t=1</subscript>(∂/∂xi)(∣∂u/∂xi∣<superscript>p-2</superscript>(∂u/∂xi))+a∣u<subscript>t</subscript>∣<superscript>q-2</superscript>u<subscript>t</subscript> = b∣u∣<superscript>r-2</superscript>u in a bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set in W<superscript>1,p</superscript><subscript>0</subscript> (Ω) and show the asymptotic behavior of the global solutions through the use of an important lemma of Komornik. [ABSTRACT FROM AUTHOR]

Subjects :: HYPERBOLIC differential equations
NUMERICAL analysis
EQUATIONS
NONLINEAR operators
FUNCTIONALS

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