Piecewise linear approximation for the dynamical Phi(4)(3) model

Zhu R, Zhu X (2020)
SCIENCE CHINA-MATHEMATICS 63(2): 381-410.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Zhu, Rongchan; Zhu, XiangchanUniBi
Abstract / Bemerkung
We 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.
Stichworte
regularity structure; space-time white noise; stochastic partial; differential equations; renormalization
Erscheinungsjahr
2020
Zeitschriftentitel
SCIENCE CHINA-MATHEMATICS
Band
63
Ausgabe
2
Seite(n)
381-410
ISSN
1674-7283
eISSN
1869-1862
Page URI
https://pub.uni-bielefeld.de/record/2941615

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Zhu R, Zhu X. Piecewise linear approximation for the dynamical Phi(4)(3) model. SCIENCE CHINA-MATHEMATICS. 2020;63(2):381-410.
Zhu, R., & Zhu, X. (2020). Piecewise linear approximation for the dynamical Phi(4)(3) model. SCIENCE CHINA-MATHEMATICS, 63(2), 381-410. doi:10.1007/s11425-017-9269-1
Zhu, R., and Zhu, X. (2020). Piecewise linear approximation for the dynamical Phi(4)(3) model. SCIENCE CHINA-MATHEMATICS 63, 381-410.
Zhu, R., & Zhu, X., 2020. Piecewise linear approximation for the dynamical Phi(4)(3) model. SCIENCE CHINA-MATHEMATICS, 63(2), p 381-410.
R. Zhu and X. Zhu, “Piecewise linear approximation for the dynamical Phi(4)(3) model”, SCIENCE CHINA-MATHEMATICS, vol. 63, 2020, pp. 381-410.
Zhu, R., Zhu, X.: Piecewise linear approximation for the dynamical Phi(4)(3) model. SCIENCE CHINA-MATHEMATICS. 63, 381-410 (2020).
Zhu, Rongchan, and Zhu, Xiangchan. “Piecewise linear approximation for the dynamical Phi(4)(3) model”. SCIENCE CHINA-MATHEMATICS 63.2 (2020): 381-410.