标题： 最大界原理针对具有低正则性积分器的Q张量梯度流 显示英文标题

标题： Maximum bound principle for Q-tensor gradient flow with low regularity integrators

摘要： 我们研究了针对向列液晶半线性抛物型方程的Q-张量模型的低正则性积分方法（LRI方法）。 利用杜哈美公式，提出了首阶和二阶时间离散格式，并严格证明这两种格式在最低正则性要求下均能保持最大值原理（MBP）和能量耗散性。 对于所提出的数值方法，建立了最优收敛率。 数值实验验证了理论结果，表明Q的特征值始终严格限制在物理范围（-1/3, 2/3）内。 显示英文摘要

摘要： We investigate low-regularity integrator (LRI) methods for the Q-tensor model governing nematic liquid-crystalline semilinear parabolic equation. First- and second-order temporal discretizations are developed using Duhamel's formula, and we rigorously prove that both schemes preserve the maximum bound principle (MBP) and energy dissipation under minimal regularity requirements. Optimal convergence rates are established for the proposed methods. Numerical experiments validate the theoretical findings, demonstrating that the eigenvalues of Q remain strictly confined within the physical range (-1/3},2/3).