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 u0(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 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2012, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |