发表机构
American University of Ras Al Khaimah（哈伊马角美国大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究三维及以上空间中双物种双刺激退化趋化模型，证明任意质量自由能解的局部存在性，并揭示解的全局存在与爆破由参数对的临界值决定。
AI 中文摘要
我们考虑维度$d \geq 3$下具有双物种和双刺激的退化趋化模型。在具有有限二阶矩和能量的可积初始数据假设下，我们证明了任意质量的自由能解（即具有某些自由能估计的弱解）的局部时间存在性。我们展示了解的定性行为由一组临界值决定：方程组中存在一个参数对的临界值，当参数对满足该临界值时存在全局时间能量解，而当参数对的临界性条件被违反时，则存在爆破的自由能解。
英文摘要
We consider a degenerate chemotaxis model with two-species and two-stimuli in dimension $d \geq 3$. Under the hypothesis of integrable initial data with finite second moment and energy, we show local-in-time existence for any mass of free-energy solutions, namely weak solutions with some free energy estimates. We exhibit that the qualitative behavior of solutions is decided by a set of critical values: there is a critical value of a parameter pair in the system of equations for which there is a global-in-time energy solution and there exist blowing-up free-energy solutions under a criticality condition is violated for the parameter pair.
