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ON THE EXISTENCE OR THE ABSENCE OF GLOBAL SOLUTIONS OF THE CAUCHY CHARACTERISTIC PROBLEM FOR SOME

Chia sẻ: Nguyen Minh Thang | Ngày: | Loại File: PDF | Số trang:18

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ON THE EXISTENCE OR THE ABSENCE OF GLOBAL SOLUTIONS OF THE CAUCHY CHARACTERISTIC PROBLEM FOR SOME NONLINEAR HYPERBOLIC EQUATIONS S. KHARIBEGASHVILI Received 20 October 2004 For wave equations with power nonlinearity we investigate the problem of the existence or nonexistence of global solutions of the Cauchy characteristic problem in the light cone of the future. 1. Statement of the problem Consider a nonlinear wave equation of the type u := ∂2 u − ∆u = f (u) + F, ∂t 2 (1.1) where f and F are the given real functions; note that f is a nonlinear and u is an unknown real...

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Nội dung Text: ON THE EXISTENCE OR THE ABSENCE OF GLOBAL SOLUTIONS OF THE CAUCHY CHARACTERISTIC PROBLEM FOR SOME

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