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<p>We consider the stochastic reaction–diffusion equation in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(1+1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> dimensions driven by multiplicative space–time white noise, with a distributional drift belonging to a Besov–Hölder space with any regularity index strictly larger than <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(-1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. We assume that the diffusion coefficient is a regular function which is bounded away from zero. By using a combination of stochastic sewing techniques and Malliavin calculus, we show that the equation admits a unique solution.</p>

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Regularisation by multiplicative noise for reaction–diffusion equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月7日

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  • Konstantinos Dareiotis,
  • Teodor Holland,
  • Khoa Lê

摘要

We consider the stochastic reaction–diffusion equation in \(1+1\) 1 + 1 dimensions driven by multiplicative space–time white noise, with a distributional drift belonging to a Besov–Hölder space with any regularity index strictly larger than \(-1\) - 1 . We assume that the diffusion coefficient is a regular function which is bounded away from zero. By using a combination of stochastic sewing techniques and Malliavin calculus, we show that the equation admits a unique solution.