Abstract In this paper, we present a numerical verification method of solutions for nonlinear parabolic initial boundary value problems. Decomposing the problem into a nonlinear part and an initial value part, we apply Nakao’s projection method, which is based on the full-discrete finite element method with constructive error estimates, to the nonlinear part and use the theoretical analysis for the heat equation to the initial value part, respectively. We show some verified examples for solutions of nonlinear problems from initial value to the neighborhood of the stationary solutions, which confirm us the actual effectiveness of our method.

中文翻译：

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非线性抛物线问题解的数值验证

摘要 在本文中，我们提出了非线性抛物线初边值问题解的数值验证方法。将问题分解为非线性部分和初值部分，我们将基于全离散有限元方法的 Nakao 投影方法应用于非线性部分，并使用热方程的理论分析来计算分别为初始值部分。我们展示了一些从初始值到平稳解邻域的非线性问题解的经过验证的例子，这证实了我们方法的实际有效性。