التفاصيل البيبلوغرافية
| العنوان: |
Spatial analyticity of solutions for a coupled system of generalized KdV equations. |
| المؤلفون: |
Atmani, A., Boukarou, A., Benterki, D., Zennir, K. |
| المصدر: |
Mathematical Methods in the Applied Sciences; Aug2024, Vol. 47 Issue 12, p10351-10372, 22p |
| مصطلحات موضوعية: |
EQUATIONS, PARTIAL differential equations, ANALYTIC spaces |
| مستخلص: |
We consider the well‐posedness of a coupled system for generalized Korteweg–de Vries (S‐gKdV) ∂tu+∂x3u+∂xupvp+1=0∂tv+∂x3v+∂xup+1vp=0,$$ \left\{\begin{array}{l}{\partial}_tu+{\partial}_x^3u+{\partial}_x\left({u}^p{v}^{p+1}\right)=0\\ {}{\partial}_tv+{\partial}_x^3v+{\partial}_x\left({u}^{p+1}{v}^p\right)=0,\end{array}\right. $$where p∈ℤ+$$ p\in {\mathrm{\mathbb{Z}}}^{+} $$ and the initial data (u0,v0)$$ \left({u}_0,{v}_0\right) $$ are analytic in a strip and then the solutions of S‐gKdV continue to be analytic in a strip the width of which will decrease as time goes to ∞$$ \infty $$, by using the standard contraction method in analytic Bourgain space. Besides, we obtain algebraic lower bounds on the decreasing rate of the uniform radius of analyticity of the solutions. [ABSTRACT FROM AUTHOR] |
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