• global nonexistence results for a class of hyperbolic systems

    جزئیات بیشتر مقاله
    • تاریخ ارائه: 1390/01/01
    • تاریخ انتشار در تی پی بین: 1390/01/01
    • تعداد بازدید: 384
    • تعداد پرسش و پاسخ ها: 0
    • شماره تماس دبیرخانه رویداد: -

    our concern in this paper is to prove blow-up results to the non-autonomous nonlinear system of wave equations

    utt − δu = a(t, x)|v|p, vtt − δv = b(t, x)|u|q, t > 0, x ∈ rn

    in any space dimension. we show that a curve. f(p, q) = 0 depending on the space dimension, on the exponents p, q and on the behavior of the functions a(t, x) and b(t, x) exists, such that all nontrivial solutions to the above system blow-up in a finite time whenever. f(p, q) > 0. our method of proof uses some estimates developed by galaktionov and pohozaev in [11] for a single non-autonomous wave equation enabling us to obtain a system of ordinary differential inequalities from which the desired result is derived. our result generalizes some important results such as the ones in del santo et al. (1996) [12] and galaktionov and pohozaev (2003) [11]. the advantage here is that our result applies to a wide variety of problems.

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