一类带扇形算子的非局部演化方程解的正则性

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-06-13 DOI:10.1016/j.jmaa.2025.129798

Nguyen Van Dac , Tran Dinh Ke , Pham Anh Toan

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引用次数: 0

摘要

研究了一类具有扇形算子和非线性扰动的非局部演化方程的抽象模型。通过半群表示，导出了可解族的正则性估计，从而证明了分数阶幂空间中相关柯西问题的全局可解性。利用不动点论证和可解性理论，得到了该问题的Hölder正则性结果。然后利用解析解理论证明了所得到的解在适当条件下是强解。给出了在整个空间中一类非线性次扩散方程的应用。

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On the regularity of solutions to a class of nonlocal evolution equations with sectorial operators

We deal with an abstract model of nonlocal evolution equations with sectorial operators and nonlinear perturbations. Regularity estimates for resolvent families are derived through semigroup representation, which allow us to show a global solvability for the associated Cauchy problem in fractional power spaces. Employing fixed point argument and resolvent theory, we obtain a Hölder regularity result for the mentioned problem. Then the analytic resolvent theory is utilized to demonstrate that the obtained solution is a strong one under appropriate conditions. An application to a class of nonlinear subdiffusion equations in the whole space is given.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.