On a model connected with the Kirchhoff equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:267

Article

Catalano, F

关键词: energy inequalities;    Von Wahl estimates;    contraction method;   

DOI  :  10.1006/jmaa.2001.7774

来源: Elsevier

【 摘 要 】

We prove a global existence result in suitable Sobolev spaces for the solution of the nonlinear Cauchy problem partial derivative(u)u(t, x) - (1 + integral(Rn) dy K(x - y)\del(y)u(t, y)\(2))Delta(x)u(t, x) = 0, u(0,x) = epsilonu(0)(x), (partial derivative(t)u)(0, x) = epsilonu(1)(x), epsilon > 0, where n > 3 is the space dimension, the initial data are C-infinity with compact support in R-n, and K(z) is a positive smooth function rapidly decreasing as \z\ --> infinity. Our approach is based on the energy estimates combined with the classical Von Wahl inequalities. (C) 2002 Elsevier Science (USA).

【 授权许可】

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