A Solution Theory for Quasilinear Singular SPDEs
A Solution Theory for Quasilinear Singular SPDEs
复制标题
拟线性奇异SPDE的解理论
DOI：
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发表时间：
2017
影响因子：
3
通讯作者：
Martin Hairer
中科院分区：
文献类型：
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作者：
M'at'e Gerencs'er;Martin Hairer
我们给出了一个构造，使我们能够建立一般拟线性随机偏微分方程的正则结构理论的局部重整化解，从而大大推广了最近的结果[1，5，11]。不严格地说，我们的构造涵盖了[3，4，7]的一般构造适用的所有类型方程的准线性变体，特别是包括由时空白色噪声驱动的具有KPZ型非线性的一维系统。在一个不太奇异和更具体的情况下，我们进一步表明，由重整化过程引入的反项是由局部泛函的解决方案。我们的建设的主要特点是，它允许利用一些现有的结果开发的半线性的情况下，使额外的参数，它需要的数量是相对较小的。© 2018作者。《纯粹与应用数学通讯》由柯朗数学科学研究所和威利期刊公司出版。
We give a construction allowing us to build local renormalized solutions to general quasilinear stochastic PDEs within the theory of regularity structures, thus greatly generalizing the recent results of [1, 5, 11]. Loosely speaking, our construction covers quasilinear variants of all classes of equations for which the general construction of [3, 4, 7] applies, including in particular one‐dimensional systems with KPZ‐type nonlinearities driven by space‐time white noise. In a less singular and more specific case, we furthermore show that the counterterms introduced by the renormalization procedure are given by local functionals of the solution. The main feature of our construction is that it allows exploitation of a number of existing results developed for the semilinear case, so that the number of additional arguments it requires is relatively small. © 2018 the Authors. Communications on Pure and Applied Mathematics is published by the Courant Institute of Mathematical Sciences and Wiley Periodicals, Inc.