報(bào)告題目： Fractional (α,p)-Laplacian Equations Driven by Superlinear Noise on R^d: Global Solvability and Invariant Measures

報(bào)告人： 王仁海 教授（貴州師范大學(xué)）

報(bào)告時間：2024年11月13日（周三）19:30-20:30

報(bào)告地點(diǎn)：2B-409

報(bào)告摘要：We consider a wide class of fractional (α,p)-Laplacian equations on R^d driven by infinite-dimensional superlinear noise. The model has three striking features: a general fractional (α,p)-Laplace operator defined via a symmetric and translation invariant kernel function K^α_p with α ∈ (0,1) and p > 2; a polynomial drift growing at an arbitrary rate q ?1 with q > 2; and a locally Lipschitz diffusion term with superlinear growth. By using a locally monotone method and a domain approximation argument, we first establish the global-in-time well-posedness and the higher-order It?’s energy equations when the diffusion term has a superlinear growth rate less than p/2 or q/2. We then prove the existence and derive the moment estimates of invariant measures of the equation under further assumptions on the superlinear diffusion terms. When the damping coefficient is suitably large, we show the unique-ness, ergodicity as well as the Wasserstein exponential mixing of invariant measures without adding any additional conditions on the superlinear noise.The idea of uniform tail-estimates is used to overcome the difficulties caused by the lack of compactness of Sobolev embeddings on unbounded domains. The dissipativeness of the drift terms and some appropriate stopping times are used to carefully deal with the superlinear diffusion terms. The analysis has no any restrictions on α ∈ (0,1), d ∈ N, p > 2 or q > 2.

This is a joint work with Professors Bixiang Wang and Penyu Chen.

報(bào)告人簡介：

王仁海, 貴州師范大學(xué)校聘教授，博士生導(dǎo)師，西南大學(xué)與美國New Mexico Institute of Mining and Technology的聯(lián)合培養(yǎng)博士，北京應(yīng)用物理與計(jì)算數(shù)學(xué)研究所博士后，長期從事無窮維隨機(jī)動力系統(tǒng)與隨機(jī)偏微分方程的研究。主持國家自然科學(xué)基金青年基金，中國博士后科學(xué)基金特別資助和面上資助，獲重慶市優(yōu)秀博士學(xué)位論文，其論文發(fā)表于在Mathematische Annalen, Mathematical Models and Methods in Applied Sciences, SIAM J. Math. Anal., Science China Mathematics, Journal of Differential Equations, Journal of Dynamics and Differential Equations, Nonlinearity, Stochastic Processes and Their Applications等刊物。