Semilinear fractional differential equations: global solutions, critical nonlinearities and comparison results
Semilinear fractional differential equations: global solutions, critical nonlinearities and comparison results
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DOI：
10.12775/tmna.2015.022
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发表时间：
2015-06
影响因子：
0.7
通讯作者：
A. Carvalho;P. M. Carvalho‐Neto;P. Marín-Rubio;B. Andrade
中科院分区：
文献类型：
--
作者：
A. Carvalho;P. M. Carvalho‐Neto;P. Marín-Rubio;B. Andrade
本文研究了关于$\alpha\in（0，1）$阶抽象分数阶Cauchy问题的几个问题。具体地，我们分析了局部温和的解决方案的存在性问题，其可能的延续到一个最大的存在区间。临界非线性和相应的正则温和的解决方案的情况下进行了研究。最后，通过建立一些一般性的比较结果，我们应用它们得到了一个由热传导理论得到的分数阶偏微分方程的整体适定性。
In this work we study several questions concerning to abstract fractional Cauchy problems of order $\alpha\in(0,1)$. Concretely, we analyze the existence of local mild solutions for the problem, and its possible continuation to a maximal interval of existence. The case of critical nonlinearities and corresponding regular mild solutions is also studied. Finally, by establishing some general comparison results, we apply them to conclude the global well-posedness of a fractional partial differential equation coming from heat conduction theory.