Global and non Global Solutions for Some Fractional Heat Equations With Pure Power Nonlinearity

Saanouni Tarek

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Global and non Global Solutions for Some Fractional Heat Equations With Pure Power Nonlinearity

机译：具有纯功率非线性的一些分数热方程的全局和非全球解决方案

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摘要

The initial value problem for a semi-linear fractional heat equation is investigated. In the focusing case, global well-posedness and exponential decay are obtained. In the focusing sign, global and non global existence of solutions are discussed via the potential well method.

机译：研究了一类半线性分数阶热方程的初值问题。在聚焦情况下，得到了全局适定性和指数衰减。在聚焦符号中，通过势阱方法讨论了解的全局存在性和非全局存在性。

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来源
《Canadian Journal of Mathematics》 |2017年第4期|共19页
作者
Saanouni Tarek;
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作者单位

Univ Tunis El Manar Fac Sci Tunis Partial Differential Equat &

Applicat LR03ES04 Tunis 2092 Tunisia;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
nonlinear fractional heat equation; global Existence; decay; blow-up;

机译：非线性分数热方程;全球存在;腐烂;爆炸;

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1. EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS FOR A SEMI-LINEAR HEAT EQUATION WITH FRACTIONAL LAPLACIAN [J] . Tan Zhong, Xu Yongqiang 数学物理学报（英文版） . 2012,第006期
2. EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTION OF NONLINEAR PARABOLIC EQUATION WITH NONLINEAR BOUNDARY CONDITION [J] . WuYONGHUI, WANGMINGXIN 数学年刊：B辑英文版 . 1995,第003期
3. Global and non Global Solutions for Some Fractional Heat Equations With Pure Power Nonlinearity [J] . Saanouni Tarek Canadian Journal of Mathematics . 2017,第4期

机译：具有纯功率非线性的一些分数热方程的全局和非全球解决方案
4. Nonexistence of Global Weak Solutions of a System of Nonlinear Wave Equations with Nonlinear Fractional Damping [J] . Mohamed Jleli, Mokhtar Kirane, Bessem Samet Journal of Function Spaces . 2020,第1期

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5. Nonexistence of Global Weak Solutions of a System of Nonlinear Wave Equations with Nonlinear Fractional Damping [J] . Mohamed Jleli, Mokhtar Kirane, Bessem Samet Journal of Function Spaces and Applications . 2020,第1期

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6. GLOBAL ATTRACTIVITY OF SOLUTIONS FOR A NONLINEAR FUNCTIONAL INTEGRAL EQUATION OF FRACTIONAL ORDER IN BANACH SPACE [C] . B.D. Karande International Conference on Mathematical Problems in Engineering and Aerospace Sciences . 2014

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7. Global Existence and Dispersion of Solutions to Nonlinear Klein-Gordon Equations with Potential. [D] . Wildman, Chad Thornton. 2014

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8. Solitary wave solutions to some nonlinear fractional evolution equations in mathematical physics [O] . H.M. Shahadat Ali, M.A. Habib, M.Mamun Miah, 2020

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9. Global dynamics of small solutions to the modified fractional Korteweg-de Vries and fractional cubic nonlinear Schrödinger equations [O] . Jean-Claude Saut, Yuexun Wang 2021

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10. Global Existence and Asymptotic Stability for a Nonlinear Integrodifferential Equation Modeling Heat Flow [R] . Brandon, D. 1989

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Global and non Global Solutions for Some Fractional Heat Equations With Pure Power Nonlinearity

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