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1.
A-调和方程障碍问题的很弱解   总被引:11,自引:0,他引:11       下载免费PDF全文
本文给出A-调和方程障碍问题很弱解的定义.使用Hodge分解等工具,得到其局部与整体高阶可积性.  相似文献
2.
A-调和方程很弱解的正则性   总被引:8,自引:0,他引:8       下载免费PDF全文
高红亚 《数学学报》2001,44(4):605-610
本文证明了二阶拟线性偏微分方程很弱解的正则性.若u是(1)的一个很弱解并属于一个合适的包含W1,p loc( )的空间,则u属于 ( ),即u是(1)通常意义下的弱解.变分积分弱极值的同样结果被得到.  相似文献
3.
弱拟正则映射的若干性质   总被引:8,自引:0,他引:8       下载免费PDF全文
高红亚 《数学学报》2002,45(1):191-196
本文应用Hodge分解,得到了弱拟正则映射的逆H  lder不等式,Lp可积性与其分量函数的弱单调性结果.  相似文献
4.
We analyse approximate solutions generated by an upwind differencescheme (of Engquist–Osher type) for nonlinear degenerateparabolic convection–diffusion equations where the nonlinearconvective flux function has a discontinuous coefficient (x)and the diffusion function A(u) is allowed to be strongly degenerate(the pure hyperbolic case is included in our setup). The mainproblem is obtaining a uniform bound on the total variationof the difference approximation u, which is a manifestationof resonance. To circumvent this analytical problem, we constructa singular mapping (, ·) such that the total variationof the transformed variable z = (, u) can be bounded uniformlyin . This establishes strong L1 compactness of z and, since(, ·) is invertible, also u. Our singular mapping isnovel in that it incorporates a contribution from the diffusionfunction A(u). We then show that the limit of a converging sequenceof difference approximations is a weak solution as well as satisfyinga Krukov-type entropy inequality. We prove that the diffusionfunction A(u) is Hölder continuous, implying that the constructedweak solution u is continuous in those regions where the diffusionis nondegenerate. Finally, some numerical experiments are presentedand discussed.  相似文献
5.
一类拟线性椭圆型方程很弱解的局部正则性   总被引:6,自引:0,他引:6  
本文考虑一类拟线性椭圆型方程的很弱解.使用Hodge分解等工具,得到了其局部正则性,推广了[1]之结果。  相似文献
6.
A New Integrable Equation with Peakon Solutions   总被引:5,自引:0,他引:5  
We consider a new partial differential equation recently obtained by Degasperis and Procesi using the method of asymptotic integrability; this equation has a form similar to the Camassa–Holm shallow water wave equation. We prove the exact integrability of the new equation by constructing its Lax pair and explain its relation to a negative flow in the Kaup–Kupershmidt hierarchy via a reciprocal transformation. The infinite sequence of conserved quantities is derived together with a proposed bi-Hamiltonian structure. The equation admits exact solutions as a superposition of multipeakons, and we describe the integrable finite-dimensional peakon dynamics and compare it with the analogous results for Camassa–Holm peakons.  相似文献
7.
ONTHEEXISTENCEANDUNIQUENESSOFTHESOLUTIONTOTHENAVIER-STOKESEQUATIONSTangXianjiang(Dept.ofMath.,Sichuanuniversity,Chengdu610064...  相似文献
8.
In this paper, we study the existence of nontrivial solutions for the following Dirichlet problem for the p-Laplacian (p > 1):where Ω is a bounded domain in Rn (A≥1) and f(x,u) is quasi-asymptotically linear with respect to |u|p-2 u at infinity. Recently it was proved that the above problem has a positive solution under the condition that f(x, s)/sp-1 is nondecrcasing with respect to s for all x ∈Ω and some others. In this paper. by improving the methods in the literature, we prove that the functional corresponding to the above problem still satisfies a weakened version of (P.S.) condition even if f(x, s)/sp-1 isn't a nondecreasing function with respect to s, and then the above problem has a nontrivial weak solution by Mountain Pass Theorem.  相似文献
9.
一类半导体方程整体弱解的存在性   总被引:3,自引:0,他引:3  
考虑激光照射的半导体方程,在初值n0,po∈L ^2(Ω)的条件下,证明了其混合初边值问题整体弱解的存在性。  相似文献
10.
We consider a free boundary problem for the equation of the one-dimensional isentropic motion with density-dependent viscosity μ =b ϱ β, whereb and β are positive constants. We prove that there exists an unique weak solution globally in time, provided that β<1/3.
Sunto Si considera un problema di frontiera libera per l’equazione del moto unidimensionale isoentropico con viscosità dipendente dalla densità secondo la legge μ =b ϱ β, doveb e β sono costanti positive. Si dimostra che esiste un’unica soluzione debole globale nel tempo, purché β<1/3.
  相似文献
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