p. 117 - 126 On the blow-up of solutions for the b-equation
M. Kodzha Received: September 8, 2011;
Revised: January 21, 2012;
Accepted: January 25, 2012
Abstract.
We establish blow-up results for a family of equations under
various classes of initial data. It turns out that it is the shape
instead of the size and smoothness of the initial data which
influences breakdown in finite time. Then, infinite propagation
speed for the shallow water equations is proved in the following
sense: the corresponding solution u(t, x) with compactly
supported initial datum u_{0}(x) does not have compact
x-support
any longer in its lifespan.
Keywords:
b-equation; blow-up.
AMS Subject classification:
Primary: 35B45, 35B65, 35Q30, 76D05
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