We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
By means of a new technique of integral representations in C n given by the authors, we establish a new abstract formula with a vector function W for smooth functions on bounded domains in C n , which is different fro...By means of a new technique of integral representations in C n given by the authors, we establish a new abstract formula with a vector function W for smooth functions on bounded domains in C n , which is different from the well-known Leray formula. This new formula eliminates the term that contains the parameter A from the classical Leray formula, and especially on some domains the uniform estimates for the $\bar \partial - equation$ are very simple. From the new Leray formula, we can obtain correspondingly many new formulas for smooth functions on many domains in C n , which are different from the classical ones, when we properly select the vector function W.展开更多
We consider Leray＇s problem on stationary Navier Stokes flows with arbitrary large fluxes in an unbounded cylinder with several exits to infinity. For a stationary Navier Stokes flow with large fluxes in the unbounde...We consider Leray＇s problem on stationary Navier Stokes flows with arbitrary large fluxes in an unbounded cylinder with several exits to infinity. For a stationary Navier Stokes flow with large fluxes in the unbounded cylinder, we prove that, if the difference between the pressure of the main flow and the pressure of the Poiseuille flow with the same flux in a branch of the cylinder remains bounded at ｜x｜→∞, then the flow behaves at infinity of the branch like the Poiseuille flow.展开更多
文摘We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19771068) Mathematical "Tian Yuan" Foundation of China (Grant No. TY10126033).
文摘By means of a new technique of integral representations in C n given by the authors, we establish a new abstract formula with a vector function W for smooth functions on bounded domains in C n , which is different from the well-known Leray formula. This new formula eliminates the term that contains the parameter A from the classical Leray formula, and especially on some domains the uniform estimates for the $\bar \partial - equation$ are very simple. From the new Leray formula, we can obtain correspondingly many new formulas for smooth functions on many domains in C n , which are different from the classical ones, when we properly select the vector function W.
基金Supported by 2012 CAS-TWAS Postdoctoral Fellowship(Grant No.3240267229)
文摘We consider Leray＇s problem on stationary Navier Stokes flows with arbitrary large fluxes in an unbounded cylinder with several exits to infinity. For a stationary Navier Stokes flow with large fluxes in the unbounded cylinder, we prove that, if the difference between the pressure of the main flow and the pressure of the Poiseuille flow with the same flux in a branch of the cylinder remains bounded at ｜x｜→∞, then the flow behaves at infinity of the branch like the Poiseuille flow.
基金Supported by Ministry of Education of Science and Technology of Important Projects(207047)Natural Science Foundation of Anhui Province of China(050460103)Key Natural Science Foundation by the Bureau of Education of Anhui Province in China(2005kj031ZD)
基金Supported by the National Natural Science Foundation of China (11071001)Anhui Provincial Natural Science Foundation (1208085MA13)+1 种基金the 211 Project of Anhui University (KJTD002B)the Key Project of Anhui Provincial Education Department (KJZ2009A2005Z)
