Cauchy problem for a damped generalized IMBq equation
In: Journal of Mathematical Physics, Jg. 52 (2011-05-01), S. 053504-53504
Online
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Zugriff:
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+1p). 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>12) and a unique global classical solution in C2([0,∞);Hs(R))(s>52), and discuss the blow up of the solution.
Titel: |
Cauchy problem for a damped generalized IMBq equation
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Autor/in / Beteiligte Person: | Chen, Guowang ; Rui, Weifang ; Chen, Xiangying |
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Zeitschrift: | Journal of Mathematical Physics, Jg. 52 (2011-05-01), S. 053504-53504 |
Veröffentlichung: | AIP Publishing, 2011 |
Medientyp: | unknown |
ISSN: | 1089-7658 (print) ; 0022-2488 (print) |
DOI: | 10.1063/1.3577956 |
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