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非线性Sobolev方程的特征-差分方法 被引量:10
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作者 由同顺 《计算数学》 CSCD 北大核心 1995年第1期13-27,共15页
非线性Sobolev方程的特征-差分方法由同顺(南开大学)THECHARACTERISTICDIFFERENCEMETHODFORANONLINEARSOBOLEVEQUATION¥YouTong-shun(Nank... 非线性Sobolev方程的特征-差分方法由同顺(南开大学)THECHARACTERISTICDIFFERENCEMETHODFORANONLINEARSOBOLEVEQUATION¥YouTong-shun(NankaiUniversity)Abst... 展开更多
关键词 索伯列夫方程 非线性 特征-差分法
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拟线性Sobolev方程的特征有限元格式及最优阶误差估计
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作者 芮洪兴 《山东大学学报(自然科学版)》 CSCD 1994年第2期137-145,共9页
考虑用沿特征线修正的有限元方法求解拟线性Sobolev方程的初边值问题,给出了两种全离散格式,并得到了最优阶L2-模及H1-模误差估计.
关键词 有限元 误差估计 索伯列夫方程
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Strichartz estimates for parabolic equations with higher order differential operators 被引量:3
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作者 DING Yong SUN XiaoChun 《Science China Mathematics》 SCIE CSCD 2015年第5期1047-1062,共16页
The present paper first obtains Strichartz estimates for parabolic equations with nonnegative elliptic operators of order 2m by using both the abstract Strichartz estimates of Keel-Tao and the Hardy-LittlewoodSobolev ... The present paper first obtains Strichartz estimates for parabolic equations with nonnegative elliptic operators of order 2m by using both the abstract Strichartz estimates of Keel-Tao and the Hardy-LittlewoodSobolev inequality. Some conclusions can be viewed as the improvements of the previously known ones. Furthermore, an endpoint homogeneous Strichartz estimates on BMOx(Rn) and a parabolic homogeneous Strichartz estimate are proved. Meanwhile, the Strichartz estimates to the Sobolev spaces and Besov spaces are generalized. Secondly, the local well-posedness and small global well-posedness of the Cauchy problem for the semilinear parabolic equations with elliptic operators of order 2m, which has a potential V(t, x) satisfying appropriate integrable conditions, are established. Finally, the local and global existence and uniqueness of regular solutions in spatial variables for the higher order elliptic Navier-Stokes system with initial data in Lr(Rn) is proved. 展开更多
关键词 Strichartz estimates elliptic Navier-Stokes equations higher order elliptic operator POTENTIAL
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