一类导数型非线性广义Tricomi方程的爆破结果

IF 1.2 3区 数学 Q1 MATHEMATICS
Sandra Lucente, Alessandro Palmieri
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引用次数: 15

摘要

本文证明了一类导数项为非线性的半线性广义Tricomi方程的一个爆破结果,即方程\(\mathcal {T}_\ell u=|\partial _t u|^p\),其中\(\mathcal {T_\ell }=\partial _t^2-t^{2\ell }\Delta \)。当非线性项的指数p小于\(\frac{\mathcal {Q}}{\mathcal {Q} -2}\)时,正柯西数据的光滑解在有限时间内爆破,其中\(\mathcal {Q}=(\ell +1)n+1\)是广义Tricomi算子\(\mathcal {T}_\ell \)的拟齐次维数。此外,我们还得到了寿命的上界估计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Blow-Up Result for a Generalized Tricomi Equation with Nonlinearity of Derivative Type

In this note, we prove a blow-up result for a semilinear generalized Tricomi equation with nonlinear term of derivative type, i.e., for the equation \(\mathcal {T}_\ell u=|\partial _t u|^p\), where \(\mathcal {T_\ell }=\partial _t^2-t^{2\ell }\Delta \). Smooth solutions blow up in finite time for positive Cauchy data when the exponent p of the nonlinear term is below \(\frac{\mathcal {Q}}{\mathcal {Q} -2}\), where \(\mathcal {Q}=(\ell +1)n+1\) is the quasi-homogeneous dimension of the generalized Tricomi operator \(\mathcal {T}_\ell \). Furthermore, we get also an upper bound estimate for the lifespan.

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来源期刊
CiteScore
2.60
自引率
0.00%
发文量
23
审稿时长
>12 weeks
期刊介绍: Milan Journal of Mathematics (MJM) publishes high quality articles from all areas of Mathematics and the Mathematical Sciences. The authors are invited to submit "articles with background", presenting a problem of current research with its history and its developments, the current state and possible future directions. The presentation should render the article of interest to a wider audience than just specialists. Many of the articles will be "invited contributions" from speakers in the "Seminario Matematico e Fisico di Milano". However, also other authors are welcome to submit articles which are in line with the "Aims and Scope" of the journal.
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