Piecewise linear approximation for the dynamical model

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2020,（2）
• 页码范围: 381-410
• 页数: 30页
• 语种: 英文

摘要

We construct a piecewise linear approximation for the dynamical Φ43 model on T3.The approximation is based on the theory of regularity structures developed by Hairer (2014).They proved that renormalization in a dynamical Φ43 model is necessary for defining the nonlinear term.In contrast to Hairer (2014),we apply piecewise linear approximations to space-time white noise,and prove that the solutions of the approximating equations converge to the solution of the dynamical Φ43 model.In this case,the renormalization corresponds to multiplying the solution by a t-dependent function,and adding it to the approximating equation.