Maykel Belluzi, Flank D. M. Bezerra, Marcelo J. D. Nascimento, Lucas A. Santos
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引用次数: 0
摘要
在本文中，我们研究了与牛顿二项式定理和扇形算子理论相关的时间抽象非自治半线性 Cauchy 问题的好求结果和高阶正则性。我们对任意阶数为 n 的抛物线问题的研究方法显然是现有文献中从未涉及过的。此外，我们还介绍了在\({\mathbb {R}}^N\) 的有界光滑域中涉及分数拉普拉奇的演化方程的应用。
A Higher-Order Non-autonomous Semilinear Parabolic Equation
In this paper, we study results of well-posedness and regularity of higher order in time abstract non-autonomous semilinear Cauchy problems associated with Newton’s binomial theorem and the theory of sectorial operators. Our approach to parabolic problems of arbitrarily order n apparently has never been addressed earlier in the existing literature. Also, we present applications to evolutionary equations involving the fractional Laplacian in bounded smooth domains of \({\mathbb {R}}^N\).
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