Cauchy problem for a damped generalized IMBq equation.

In this paper, we prove that the Cauchy problem for the following damped generalized IMBq equation, utt-uxx-uxxtt+ν2uxxt=f(u)xx,x∈R,t>0, admits a unique global generalized solution in C3([0,∞);Wm,p(R)∩L∞(R)∩L2(R))(1≤p≤∞,m≥0) and a unique global classical solution in C3([0,∞);Wm,p(R)∩L∞(R)∩L2(R))(m>2+<FRACTION><NUM>1</NUM><DEN>p</DEN></FRACTION>). Moreover, the blow up of the solution for the Cauchy problem of damped generalized IMBq equation is studied. We also prove that the Cauchy problem of the above-mentioned equation has a unique global generalized solution in C2([0,∞);Hs(R))(s><FRACTION><NUM>1</NUM><DEN>2</DEN></FRACTION>) and a unique global classical solution in C2([0,∞);Hs(R))(s><FRACTION><NUM>5</NUM><DEN>2</DEN></FRACTION>), and discuss the blow up of the solution. [ABSTRACT FROM AUTHOR]