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Blowup of solutions for improved Boussinesq type equation
- Source :
-
Journal of Mathematical Analysis & Applications . Feb2003, Vol. 278 Issue 2, p335. 19p. - Publication Year :
- 2003
-
Abstract
- The paper studies the existence and uniqueness of local solutions and the blowup of solutions to the initial boundary value problem for improved Boussinesq type equation <f>utt−uxx−uxxtt=σ(u)xx</f>. By a Galerkin approximation scheme combined with the continuation of solutions step by step and the Fourier transform method, it proves that under rather mild conditions on initial data, the above-mentioned problem admits a unique generalized solution <f>u∈W2,∞([0,T];H2(0,1))</f> as long as <f>σ∈C2(R)</f>. In particular, when <f>σ(s)=asp</f>, where <f>a≠0</f> is a real number and <f>p>1</f> is an integer, specially <f>a<0</f> if <f>p</f> is an odd number, the solution blows up in finite time. Moreover, two examples of blowup are obtained numerically. [Copyright &y& Elsevier]
- Subjects :
- *BOUNDARY value problems
*ALGEBRAIC geometry
Subjects
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 278
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 9405094
- Full Text :
- https://doi.org/10.1016/S0022-247X(02)00516-4