The well-posedness of the global solution for a damped euler-bernoulli equation

Abstract

In this paper, we study the well-posedness of the global solution to the following damped Euler-Bernoulli equation utt+ auxxxx+ 2but+ cu = f(u), t≥0, x; ε [0, + ∞). For the case f(u) = u2, the existence and uniqueness of the global solution to an initial value problem of the equation are established in the space C([0,+∞),L2([0,+∞)))∩C1([0,+∞), H-1([0,+∞))). For the case where f(u) is a polynomial, we find that the well-posedness can be established in the Sobolev space C([0, +∞), Hs([0, +∞))) ∩ C1([0, +∞), Hs-1([0, +∞))) (s > 1/2). © 2010 Academic Publications.