Abstract fractional Cauchy problems with almost sectorial operators
Abstract fractional Cauchy problems with almost sectorial operators
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DOI：
10.1016/j.jde.2011.08.048
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发表时间：
2012
影响因子：
2.4
通讯作者：
Rong-Nian Wang;De-Han Chen;Ti‐Jun Xiao
中科院分区：
文献类型：
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作者：
Rong-Nian Wang;De-Han Chen;Ti‐Jun Xiao
我们关注的是线性和半线性时间分数阶发展方程的柯西问题，在线性部分中包含一个线性算子A，其预解式满足复平面一个扇区中的增长估计−γ（−1<γ<0），例如，当考虑具有细柄的哑铃极限域或Hölder连续函数空间中的偏微分算子时，就会出现这种情况。利用广义Mittag-Leffler型函数和与A相关的预解算子构造了一对算子族，并对这对算子族的性质进行了深入的分析，得到了Cauchy问题的温和解和经典解的存在唯一性.此外，我们提出了三个例子来说明我们的结果的可行性。
Of concern are the Cauchy problems for linear and semilinear time fractional evolution equations involving in the linear part, a linear operator A whose resolvent satisfies the estimate of growth −γ(−1<γ<0) in a sector of the complex plane, which occurs when one considers, for instance, the partial differential operators in the limit domain of dumb-bell with a thin handle or in the space of Hölder continuous functions. By constructing a pair of families of operators in terms of the generalized Mittag-Leffler-type functions and the resolvent operators associated with A (for the first time), and a deep analysis on the properties for these families, we obtain the existence and uniqueness of mild solutions and classical solutions to the Cauchy problems. Moreover, we present three examples to illustrate the feasibility of our results.