Global existence and uniform stabilization of a generalized dissipative Klein-Gordon equation type with boundary damping

Journal Article · Tue Feb 15 00:00:00 EST 2011 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3544046· OSTI ID:21501274

Zaiyun, Zhang; Xiujin, Miao; Yuezhong, Chen ^[1]; Zhenhai, Liu ^[2]

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1. School of Mathematical Science and Computing Technology, Central South University, Shaoshan Road, Changsha, 410075, Hunan Province (China)
2. School of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, Guangxi Province (China)

In this paper, we prove the existence, uniqueness, and uniform stability of strong and weak solutions of the nonlinear generalized Klein-Gordon equation (1.1){sub 1} (see Sec. I) in bounded domains with nonlinear damped boundary conditions given by (1.1){sub 3} (see Sec. I) with some restrictions on function f(u), h({nabla}u), g(u{sub t}), and b(x), we prove the existence and uniqueness by means of nonlinear semigroup method and obtain the uniform stabilization by using the multiplier technique.

• OSTI ID: 21501274
• Journal Information: Journal of Mathematical Physics, Vol. 52, Issue 2; Other Information: DOI: 10.1063/1.3544046; (c) 2011 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
AXIOMATIC FIELD THEORY
BOUNDARY CONDITIONS
FUNCTIONS
KLEIN-GORDON EQUATION
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
RELATIVISTIC RANGE
DIFFERENTIAL EQUATIONS
ENERGY RANGE
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
WAVE EQUATIONS