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In this paper,the authors investigate the first boundary value problem for equations ofthe formwithAn existence theorem of solution in BV_(1,1/2)(Q_T)is proved.The principal condition is thatthere exists δ>0 such that for any(x,t)∈Q_T,|u|≤Ma~(ij)(u,x,t)ξ_iξ_j-δ(a_(x_θ)~(ij)(u,x,t)ξ_i)~2≥0.a, ~=1 相似文献
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In this note we consider the following Cauchy problem: u t=div(| u| p- 2 u) ,(x,t)∈ QT=Rn × (0 ,T) ,u(x,0 ) =u0 (x)∈ L∞ (RN) ,x∈ RN,(1 )where p>2 is a constant.It is well known that there exists a solution u∈ Cαloc(QT)∩L∞ (QT) to (1 ) ,with uxj∈ Cβ,β/ 2loc (QT) ,j=1 ,2 ,… ,N (see [1 ] ,[2 ] ) .The proofs of uxj∈Cβ,β/ 2loc (QT) are very complicated and difficult.In this note we use another approach toprove the Holder continuity.We proveuxj∈ Cβ,β/ (1 +β)loc (QT… 相似文献
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UNIQUENESS OF SOLUTIONS FOR HIGHER DIMENSIONAL QUASILINEAR DEGENERATE PARABOLIC EQUATION 总被引:1,自引:0,他引:1
Zhao Junning 《数学年刊B辑(英文版)》1992,13(2):129-136
This paper studies the uniqueness of generalized solutions for the first boundary value problem of the form where A_u≥0.It is proved that if u∈BV_x(Q_T) and A(u, x, t) is strictly increasing with respect to u, the solution is unique. 相似文献