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

Journal Article · Tue Feb 15 04:00:00 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, Journal Name: Journal of Mathematical Physics Journal Issue: 2 Vol. 52; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

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