Non-linear rough heat equations

By A. Deya, Massimiliano Gubinelli, Samy Tindel. 2009

89 citations recorded by the source corpus.

This article is devoted to define and solve an evolution equation of the form dyt = Δytdt + dXt (yt), where Δ stands for the Laplace operator on a space of the form $${L^p(\mathbb R^n)}$$, and X is a finite dimensional noisy nonlinearity whose typical form is given by $${X_t(\varphi)=\sum_{i=1}^N \, x^{i}_t f_i(\varphi)}$$, where each x = (x(1), … , x(N)) is a γ-Hölder function generating a rough path and each fi is a smooth enough function defined on $${L^p(\mathbb R^n)}$$. The generalization of the usual rough path theory allowing to cope with such kind of system is carefully constructed.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/75fc4e626dad8a9f2e7313578c3f8c0ec2ba5d66

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In Computational Theory and Mathematics

  1. Samy Tindel
  2. Yaozhong Hu
  3. Martina Hofmanov'a
  4. Massimiliano Gubinelli
  5. David Nualart
  6. Jingyu Huang
  7. Franco Flandoli

In Mathematical Physics

  1. Samy Tindel
  2. David Nualart
  3. Yaozhong Hu
  4. A. Deya
  5. Jingyu Huang
  6. Massimiliano Gubinelli
  7. Martina Hofmanov'a
  8. Jorge A. León

In Numerical Analysis

  1. Samy Tindel
  2. Martina Hofmanov'a
  3. Massimiliano Gubinelli
  4. Yaozhong Hu

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