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Piecewise linear approximation for the dynamical Phi(4)(3) model
Zhu, Rongchan1,2; Zhu, Xiangchan2,3,4
AbstractWe construct a piecewise linear approximation for the dynamical 43 model on T3. The approximation is based on the theory of regularity structures developed by Hairer (2014). They proved that renormalization in a dynamical 43 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 43 model. In this case, the renormalization corresponds to multiplying the solution by a t-dependent function, and adding it to the approximating equation.
Keywordregularity structure space-time white noise stochastic partial differential equations renormalization
Indexed BySCI
Funding ProjectNational Natural Science Foundation of China[11671035] ; National Natural Science Foundation of China[11771037]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000511922000007
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Document Type期刊论文
Corresponding AuthorZhu, Xiangchan
Affiliation1.Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China
2.Univ Bielefeld, Dept Math, D-33615 Bielefeld, Germany
3.Beijing Jiaotong Univ, Sch Sci, Beijing 100044, Peoples R China
4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Zhu, Rongchan,Zhu, Xiangchan. Piecewise linear approximation for the dynamical Phi(4)(3) model[J]. SCIENCE CHINA-MATHEMATICS,2020,63(2):381-410.
APA Zhu, Rongchan,&Zhu, Xiangchan.(2020).Piecewise linear approximation for the dynamical Phi(4)(3) model.SCIENCE CHINA-MATHEMATICS,63(2),381-410.
MLA Zhu, Rongchan,et al."Piecewise linear approximation for the dynamical Phi(4)(3) model".SCIENCE CHINA-MATHEMATICS 63.2(2020):381-410.
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