تقرير
Quantitative instability for stochastic scalar reaction-diffusion equations
| العنوان: | Quantitative instability for stochastic scalar reaction-diffusion equations |
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| المؤلفون: | Blessing, Alexandra, Rosati, Tommaso |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Probability, Mathematics - Analysis of PDEs, 60H15 |
| الوصف: | This work studies the instability of stochastic scalar reaction diffusion equations, driven by a multiplicative noise that is white in time and smooth in space, near to zero, which is assumed to be a fixed point for the equation. We prove that if the Lyapunov exponent at zero is positive, then the flow of non-zero solutions admits uniform bounds on small negative moments. The proof builds on ideas from stochastic homogenisation. We require suitable corrector estimates for the solution to a Poisson problem involving an infinite-dimensional projective process, together with a linearisation step that hinges on quantitative parametrix-like arguments. Overall, we are able to construct an appropriate Lyapunov functional for the nonlinear dynamics and address some problems left open in the literature. Comment: 48 Pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.04651 |
| رقم الأكسشن: | edsarx.2406.04651 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |