Well-posedness of Kimura Equation in Genetic Drift

主講人：陳新富 西南財經(jīng)大學(xué)特聘教授

時間：2023年7月5日10：00

地點：三號樓332室

舉辦單位：數(shù)理學(xué)院

主講人介紹：陳新富，現(xiàn)為西南財經(jīng)大學(xué)特聘教授。1980年至1986年就讀北京大學(xué)數(shù)學(xué)本科、碩士研究生，1991年獲美國明尼蘇達大學(xué)博士，師從美國藝術(shù)與科學(xué)院院士A. Friedman。曾獲得Sloan研究獎及多次美國自然科學(xué)基金。陳教授研究領(lǐng)域廣泛，包括非線性拋物型和橢圓型偏微分方程、自由邊值問題、界面動力學(xué)等，取得了一系列國際同行認可的重要成果。這些成果發(fā)表在 Arch. Ration. Mech. Anal., J. Differential Geom., Math. Ann., Trans. Amer. Math. Soc., SIAM J. Math. Anal., SIAM J. Appl. Math., Calc. Var. Partial Differential Equations等一流數(shù)學(xué)期刊上。

內(nèi)容介紹：We present a rigorous derivation of the continuum Kimura equation from a discrete Wright–Fisher genetic drift model. We show that boundary conditions are not needed for and cannot be imposed on the resulting degenerate diffusion problem. To this end, we reformulate the concept of weak solutions. In doing so, we find that the extension of the Kimura equation to the whole space should be the continuum limit that carries over the biologically relevant statistic information from the discrete model; namely, the conservation laws embedded in the discrete model are now self-contained in the continuum problem, without imposing any extra boundary conditions or integral constraints. We establish a well-posedness (existence, uniqueness, regularity, stability) theory and especially prove the analyticity of the solution. Our arguments build an intrinsic connection between the genetic fixation probability and a stochastic process with two absorbing barriers.