准线性奇异 SPDE 的正则结构

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

Archive for Rational Mechanics and Analysis Pub Date : 2024-11-29 DOI:10.1007/s00205-024-02069-6

I. Bailleul, M. Hoshino, S. Kusuoka

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引用次数: 0

摘要

我们证明了准线性广义（KPZ）方程的正则结构表述的好求特性，并给出了全亚临界体制下重正则化方程的明确形式。在与非平移不变算子相关的 BPHZ 模型收敛的假设下，我们得到了正则化重正则化方程解的收敛结果。这一条件结果涵盖了时空白噪声情况。

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Regularity Structures for Quasilinear Singular SPDEs

We prove the well-posed character of a regularity structure formulation of the quasilinear generalized (KPZ) equation and give an explicit form for a renormalized equation in the full subcritical regime. Under the assumption that the BPHZ models associated with a non-translation invariant operator converge, we obtain a convergence result for the solutions of the regularized renormalized equations. This conditional result covers the spacetime white noise case.

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来源期刊

Archive for Rational Mechanics and Analysis 物理-力学

CiteScore

5.10

自引率

8.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.