Abstract This work studies a parabolic-parabolic chemotactic PDE's system which describes the evolution of a biological population “U” and a chemical substance “V”, using a Generalized Finite Difference Method, in a two dimensional bounded domain with regular boundary. In a previous paper [12] , the authors asserted global classical solvability and periodic asymptotic behavior for the continuous system in 2D. In this continuous work, a rigorous proof of the global classical solvability to the discretization of the model proposed in [12] is presented in two dimensional space. Numerical experiments concerning the convergence in space and in time, and long-time simulations are presented in order to illustrate the accuracy, efficiency and robustness of the developed numerical algorithms.

中文翻译：

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使用广义有限差分法求解具有周期性渐近行为的完全抛物线趋化系统

摘要 这项工作研究了抛物线-抛物线趋化偏微分方程系统，该系统使用广义有限差分方法在具有规则边界的二维有界域中描述了生物种群“U”和化学物质“V”的演化。在之前的一篇论文 [12] 中，作者断言了二维连续系统的全局经典可解性和周期性渐近行为。在这项连续的工作中，在二维空间中提出了 [12] 中提出的模型离散化的全局经典可解性的严格证明。提出了关于空间和时间收敛的数值实验，以及长时间的模拟，以说明所开发数值算法的准确性、效率和鲁棒性。