On the nonlinear wave equation utt−B(∥ux∥2)uxx=f(x,t,u,ux,ut,∥ux∥2) associated with the mixed homogeneous conditions
In: Nonlinear Analysis: Theory, Methods & Applications, Jg. 55 (2003-11-01), S. 493-519
Online
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Zugriff:
In this paper, we consider the following nonlinear wave equation: (1) utt−B(∥ux∥2)uxx=f(x,t,u,ux,ut,∥ux∥2),x∈(0,1),00,B1∈CN(R+),B1⩾0,f∈CN+1([0,1]×R+×R3×R+) and f1∈CN([0,1]×R+×R3×R+) we obtain from the following equation: utt−[B(∥ux∥2)+eB1(∥ux∥2)]uxx=f(x,t,u,ux,ut,∥ux∥2)+ef1(x,t,u,ux,ut,∥ux∥2) associated to (2), (3) a weak solution ue(x,t) having an asymptotic expansion of order N+1 in e, for e sufficiently small.
| Titel: |
On the nonlinear wave equation utt−B(∥ux∥2)uxx=f(x,t,u,ux,ut,∥ux∥2) associated with the mixed homogeneous conditions
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| Autor/in / Beteiligte Person: | Bui Tien Dung ; Nguyen Thanh Long |
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| Zeitschrift: | Nonlinear Analysis: Theory, Methods & Applications, Jg. 55 (2003-11-01), S. 493-519 |
| Veröffentlichung: | Elsevier BV, 2003 |
| Medientyp: | unknown |
| ISSN: | 0362-546X (print) |
| DOI: | 10.1016/j.na.2003.07.002 |
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