A class of fractional parabolic reaction–diffusion systems with control of total mass: theory and numerics

Pub Date : 2024-02-26 DOI:10.1007/s11868-023-00576-w

引用次数: 0

Abstract

In this paper, we prove global-in-time existence of strong solutions to a class of fractional parabolic reaction–diffusion systems posed in a bounded domain of \(\mathbb {R}^N\) . The nonlinear reactive terms are assumed to satisfy natural structure conditions which provide nonnegativity of the solutions and uniform control of the total mass. The diffusion operators are of type \(u_i\mapsto d_i(-\Delta )^s u_i\) where \(0<s<1\) . Global existence of strong solutions is proved under the assumption that the nonlinearities are at most of polynomial growth. Our results extend previous results obtained when the diffusion operators are of type \(u_i\mapsto -d_i\Delta u_i\) . On the other hand, we use numerical simulations to examine the global existence of solutions to systems with exponentially growing right-hand sides, which remains so far an open theoretical question even in the case \(s=1\) .

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一类具有总质量控制的分数抛物线反应扩散系统：理论与数值计算

摘要在本文中，我们证明了一类分数抛物面反应扩散系统在 \(\mathbb {R}^N\) 有界域中的强解的全局实时存在性。假定非线性反应项满足自然结构条件，这些条件提供了解的非负性和总质量的均匀控制。扩散算子为 \(u_i\mapsto d_i(-\Delta )^s u_i\) 类型，其中 \(0<s<1\) 。在非线性最多为多项式增长的假设下，证明了强解的全局存在性。我们的结果扩展了之前在扩散算子为 \(u_i\mapsto -d_i\Delta u_i\) 类型时获得的结果。另一方面，我们利用数值模拟研究了具有指数增长右边的系统解的全局存在性，即使在 \(s=1\) 的情况下，这迄今为止仍然是一个开放的理论问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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