非均匀介质中格点Fisher-KPP方程广义行波解的稳定性和唯一性
Stability and uniqueness of generalized traveling waves of lattice Fisher-KPP equations in heterogeneous media
摘要：
本文研究了具有一般时空依赖性的格点Fisher-KPP方程广义行波解的稳定性和唯一性。我们首先证明了这类方程严格正整解的存在性、唯一性和稳定性。其次，我们证明了连接唯一严格正整解和平凡解零的广义行波的稳定性和唯一性。然后利用一般稳定性和唯一性定理，证明了时空周期介质中格子Fisher-KPP方程周期行波解的存在性、稳定性和唯一性，以及时间非均匀介质中格子Fisher-KPP方程广义行波解的存在性、稳定性和唯一性.本文建立的一般稳定性结果表明，在许多情况下得到的广义行波在适合扰动下是渐近稳定的。
英文摘要：
In this paper, we investigate the stability and uniqueness of generalized traveling wave solutions of lattice Fisher-KPP equations with general time and space dependence. We first show the existence, uniqueness, and stability of strictly positive entire solutions of such equations. Next, we show the stability and uniqueness of generalized traveling waves connecting the unique strictly positive entire solution and the trivial solution zero. Applying the general stability and uniqueness theorem, we then prove the existence, stability and uniqueness of periodic traveling wave solutions of lattice Fisher-KPP equations in time and space periodic media, and the existence, stability and uniqueness of generalized traveling wave solutions of lattice Fisher-KPP equations in time heterogeneous media. The general stability result established in this paper implies that the generalized traveling waves obtained in many cases are asymptotically stable under well-fitted perturbation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
