REGULARITY OF ENTROPY SOLUTIONS TO NONCONVEX SCALAR CONSERVATION LAWS WITH MONOTONE INITIAL DATA

We prove that for a given strictly increasing initial datum in Ck, the solution of the initial value problem is piecewise Ck smooth except for flux functions of nonconvex conservation laws in a certain subset of C^k＋1 of first category, defined in the range of the initial datum.     

Quasi-sure Flows Associated with Vector Fields of Low Regularity

The authors construct a solution Ut（x） associated with a vector field on the Wiener space for all initial values except in a 1-slim set and obtain the 1-quasi-sure flow property where the vector field is a sum of a skew-adjoint operator not necessarily bounded and a nonlinear part with low regularity, namely one-fold differentiability. Besides, the equivalence of capacities under the transformations of the Wiener space induced by the solutions is obtained.     

RESEARCH ANNOUNCEMENTS On a Singular Diffusion Equation in Nondivergence Form

This paper studies a singular diffusion equation in nondivergence form with the Dirichlet boundary value and initial value Here p > 1,Ω(?) RN is a bounded domain with appropriately smooth boundary (?)Ω, and φ(u) satisfies the following condition (1.1) aries some models describing physical phenomenon. For example, if φ(u) = uq with q ∈[0,1), then (1.1) can be written in divergence form after the change of variables (provided     

GLOBAL STABILITY OF SOLUTIONS WITH DISCONTINUOUS INITIAL DATA CONTAINING VACUUM STATES FOR THE RELATIVISTIC EULER EQUATIONS

The global stability of Lipschitz continuous solutions with discontinuous initial data for the relativistic Euler equations is established in a broad class of entropy solutions in L∞containing vacuum states. As a corollary, the uniqueness of Lipschitz solutions with discontinuous initial data is obtained in the broad class of entropy solutions in     

高阶Broer-Kaup(BK)方程组的新精确解

利用扩展齐次平衡法,我们得到了1+1维和2+1维高阶BK方程组新的孤子解和无穷多有理函数解,尤其是求出了初始值问题解的封闭形式.     

Solution to Nonlinear Parabolic Equations Related to the P-Laplacian

Consider the following Cauchy problem:u_t = div(|▽u ~m |~ p-2▽u~m),(x,t) ∈ST=R~N ×(0,T),u(x,0) = μ,x ∈R~N,where 1相似文献   

变系数非线性递归序列的极限

对形如F_(n+p)=(sum from to i=1 to p)a_i(n)F_(n+i-1)~(b_i),n≥1的变系数非线性递归序列{F_n}的极限问题进行了研究,给出了在满足一定条件时,序列{F_n}收敛且极限值与初始值F_i>0,i=1,2,…,p无关.     

EXISTENCE RESULTS FOR FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH RIEMANN-LIOUVILLE DERIVATIVE

In this paper, using the contracting mapping principle and the monotone iterative method, we consider the existence of solution to the initial value problem of fractional functional differential equations with Riemann-Liouville derivative.     

一类非线性递归序列的极限

探讨了形如Fn+2=a1Fnb1+1+a2Fbn2+1,n 1的非线性递归序列{Fn}的极限问题,给出了在满足一定条件时,序列{Fn}的极限值与初始值无关.