Title of article :
Blowup of solutions for improved Boussinesq
type equation ✩
Author/Authors :
Zhijian Yang ? and Xia Wang، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 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 ut t −uxx −uxxtt = σ(u)xx.
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 abovementioned
problem admits a unique generalized solution u ∈ W2,∞([0,T ];H2(0, 1)) as long as
σ ∈ C2(R). In particular, when σ(s) = asp, where a = 0 is a real number and p >1 is an integer,
specially a <0 if p is an odd number, the solution blows up in finite time. Moreover, two examples
of blowup are obtained numerically.
2003 Elsevier Science (USA). All rights reserved.
Keywords :
Improved Boussinesq equation , Blowup of solutions , initial boundary value problem , Local solution
Journal title :
Journal of Mathematical Analysis and Applications
Journal title :
Journal of Mathematical Analysis and Applications