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<p>In this paper, we accomplish the existence and stability of the solution of a class of delay rough partial differential equations (DRPDEs). Moreover, we prove that the solution of DRPDEs can converge to that of RPDEs as the delay tends to zero. These results can be applied to study a class of delayed stochastic partial differential equations (SPDEs) driven by Brownian motion and fractional Brownian motion with Hurst parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \in (\frac{1}{3},\frac{1}{2})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> <mo>,</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Delay Rough Evolution Equations

  • 期刊论文

  • 发表日期：

    2025年12月5日

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  • Shiduo Qu,
  • Hongjun Gao

摘要

In this paper, we accomplish the existence and stability of the solution of a class of delay rough partial differential equations (DRPDEs). Moreover, we prove that the solution of DRPDEs can converge to that of RPDEs as the delay tends to zero. These results can be applied to study a class of delayed stochastic partial differential equations (SPDEs) driven by Brownian motion and fractional Brownian motion with Hurst parameter \(\alpha \in (\frac{1}{3},\frac{1}{2})\) α ∈ ( 1 3 , 1 2 ) .