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LOCAL AND GLOBAL SOLVABILITY FOR A NONLINEAR DIFFUSION MODEL WITH FRACTIONAL LAPLACIAN OPERATORS IN BESOV TYPE SPACES

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发表日期：

2025年7月21日

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Ahmed El Idrissi,
Brahim El Boukari,
Jalila El Ghordaf

摘要

This paper considers a model of nonlinear diffusion with fractional Laplacian operators in homogeneous Besov spaces. By using the smoothing effect of the heat semigroup and the Littlewood-Paley theory, we obtain, with a sufficient condition, the local solution of this model. Moreover, we get the global solution for small initial data in the critical Besov spaces $ \dot{B}_{p\infty }^{-2m+\frac{d}{p}}(\mathbb {R}^d)$ ${\dot{B}}_{p \infty}^{- 2 m + \frac{d}{p}} (R^{d})$ with $\frac{1}{2}<m< 1$ $\frac{1}{2} < m < 1$ and $\max \left\{ 1,\frac{d}{2m}\right\}< p<\infty $ $max \{1, \frac{d}{2 m}\} < p < \infty$ .