欢迎您！东篱公司
退出
-
申报数据库
-
立项数据库
-
成果数据库
-
项目获奖数据库
位置：立项数据库 > 立项详情页
中文摘要：
本项目研究两个方面的问题（1）肿瘤生长的自由边界问题,（2）非线性发展方程。这是两类在现代医学、生物学和物理学等领域有重要应用背景的偏微分方程问题。对于肿瘤生长的自由边界问题，我们对带Stokes方程的流体型肿瘤模型、tumor cord 肿瘤模型和multi-layer肿瘤模型做了严格的数学分析，证明了这些自由边界问题都在适当的函数空间中是适定的，在此基础上研究了解在时间趋于无穷时的渐近性态，证明了当表面张力系数大于一个临界值时，通常稳态解是渐近稳定的。对于非线性发展方程,我们研究了Benjamin-Ono方程、KdV方程和mKdV方程等几类经典色散方程的解映射在其临界适定性空间中的弱连续性和Navier-Stokes-Nernst-Planck-Poisson方程、Debye-Huckel方程、液晶流方程、各向异性的高阶非线性Schrodinger方程、广义Davey-Stewartson方程、广义Davey-Stewartson方程、Ostrovsky-Stepanyams- Tsimring方程等一系列非线性发展方程的初值问题在适当函数空间中的局部与整体适定性。
结论摘要：
英文主题词Tumor model; Free boundary problem; Evolution equation; Well-posedness; Asymptotic behavior.
成果综合统计
期刊论文
会议论文
专利
获奖
著作
期刊论文
Well-posedness of the Cauchy problem for Ostrovsky, Stepanyams and Tsimring equation with low regula
ASYMPTOTIC STABILITY OF THE STATIONARY SOLUTION FOR A HYPERBOLIC FREE BOUNDARY PROBLEM MODELING TUMO
WELL-POSEDNESS AND STABILITY OF A MULTIDIMENSIONAL MOVING BOUNDARY PROBLEM MODELING THE GROWTH OF TU
Asymptotic behaviour of solutions of a multidimensional moving boundary problem modeling tumor growt
Asymptotic behavior of solutions for parabolic differential equations with invariance and applicatio
Global well-posedness of a dissipative system arising in electrohydrodynamics in negative-order Beso
Well-posedness for the Navier–Stokes–Nernst–Planck–Poisson system in Triebel–Lizorkin space and Beso
Lie group action and stability analysis of stationary solutions for a free boundary problem modellin
Asymptotic behavior of solutions of a free boundary problem modelling the growth of tumors with Stok
Asymptotic stability of stationary solutions of a free boundary problem modeling the growth of tumor
Analysis of an elliptic–parabolic free boundary problem modelling the growth of non-necrotic tumor c
Existence and asymptotic behavior of solutions to a moving boundary problem modeling the growth of m
Well-posedness of the Cauchy problem of high dimension non-isotropic fourth-order Schr?dinger equati
Local well-posedness of the Ostrovsky, Stepanyams and Tsimring equation in Sobolev spaces of negativ
相关项目
崔尚斌的项目