A Nonlinear Degenerate Parabolic Equation

ＡＮｏｎｌｉｎｅａｒＤｅｇｅｎｅｒａｔｅＰａｒａｂｏｌｉｃＥｑｕａｔｉｏｎ￥ＪｉａｎｇＹｉｎｇｊｉｅ（ＪｉａｏｚｕｏＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒｗｅｓｔｕｄｙａｎｏｎｌｉｎｅｒｄｅｇｅｎｅｒａｔｅｐａｒａｂｏｌｉｃｅ...     

On the Relation between the Properties of a Degenerate Linear-Quadratic Control Problem and the Euler–Poisson Equation

Computational Mathematics and Mathematical Physics - A quadratic functional with linear constraints in the form of differential equations with identically degenerate matrices multiplying the...     

On the Necessary and Sufficient Condition of Existence of Solution to Cauchy problem of a Class of Degenerate Equation

In this paper, we discuss the existence of the solution to the Cauchy problem: L_p~ku≡u_(xx)-x~(2k)u_(tt) Px~(k-1)u_t=f(x,t),t≥0, (1) (A_k) u(x,0)=ψ_1(x), u_t(x,0)=ψ_2(x), (2)where κ=2i 1, i=0,1,2,…,P R=(-∞, ∞), ψ_1(x),ψ_2(x)∈C~∞(R), f(x,t) ∈C~∞(R_2~ ),R_2~ ={(x, t)∈R~2|t≥0}.If κ=1, the uniqueness and existence of solution to the Cauchy problem(A_κ) was entirely solved by [1-3], if κ>1, A. Menikoff proved that the C~∞     

Propagation of Perturbations of Solutions for a Doubly Degenerate Nonlinear Parabolic Equation

ＰｒｏｐａｇａｔｉｏｎｏｆＰｅｒｔｕｒｂａｔｉｏｎｓｏｆＳｏｌｕｔｉｏｎｓｆｏｒａＤｏｕｂｌｙＤｅｇｅｎｅｒａｔｅＮｏｎｌｉｎｅａｒＰａｒａｂｏｌｉｃＥｑｕａｔｉｏｎＷａｎｇＹｉｆｕ（王一夫）；ＹｉｎＪｉｎｇｘｕｅ（尹景学）（Ｄｅｐａｒｔｍｅｎｔｏｆ...     

On the Solution of the Feigenbaum's Functional Equation

（陈芳跃）ＯｎｔｈｅＳｏｌｕｔｉｏｎｏｆｔｈｅＦｅｉｇｅｎｂａｕｍ＇ｓＦｕｎｃｔｉｏｎａｌＥｑｕａｔｉｏｎ￥ＣｈｅｎＦａｈｇｙｕｅ（Ｄａｐｔ．ｏｆＭａｔｈ．，ＺｈｅｊｉａｎｇＮｏｒｍａｌＵｎｉｖ．，Ｊｉｎｈｕａ，Ｚｈｅｊｉａｎｇ，３２１００４）Ｉｎｔ...     

Holder Continuity for Solutions of Degenerate Parabolic Equation with Two Degenerate Points

In this paper we discuss the quasilinear parabolic equationU_■=▽(u~u(1-u)~β.Vu)+■(x,t.u)▽u+C(x,t,u)which is degenerate at u =0 and u=1.Let u(x,t)be a weak solution of the equation satisfying0相似文献   

On the Initial Value Problem for a Parabolic Monge-Ampere Equation

From the theory of optimal investment in mathematical finance,the following initial valueproblem for a parabolic Monge—Ampere equation was derived in吣=0, (8,Y)∈[0,T)×R,where V=y(s,Y)is the unknown function,r,b,仃are given0,b—r>0,and in a typical case,the function g(y)is given by g(v)=1一e-,ky,constants with r≥0,盯>(2)where A iS a positive constant.The practice meaning of the above parameters and functionscan be found in Chapters 2 and 4 in[1】.From the mathematical point of view,the …     

Extinction and Positivity for a Doubly Nonlinear Degenerate Parabolic Equation

The aims of this paper are to discuss the extinction and positivity for the solution of the initial boundary value problem and Cauchy problem of ut = div（[↓△u^m｜p-2↓△u^m）. It is proved that the weak solution will be extinct for 1 〈 p ≤ 1 ＋ 1/m and will be positive for p 〉 1 ＋ 1/m for large t, where m 〉 0.     

On the Equation and the Number of Solution of Znam's Problem

§1. In 1972,St.Znam posed the problem whether for every s>1 thereexist integers x_i>1,i=1,…,s such that x_i is a proper divisor of the numberx_1…x_(i-1)x_(i 1)…x_s 1 for i=1,…, s.Without loss of generality, we may assume1相似文献   

Blow Up for Solutions of Nonlinear Doubly Degenerate Parabolic Equation

Ｂｌｏｗ　Ｕｐ　ｆｏｒ　Ｓｏｌｕｔｉｏｎｓ　ｏｆ　Ｎｏｎｌｉｎｅａｒ　Ｄｏｕｂｌｙ　Ｄｅｇｅｎｅｒａｔｅ　Ｐａｒａｂｏｌｉｃ　ＥｑｕａｔｉｏｎＢｌｏｗＵｐｆｏｒＳｏｌｕｔｉｏｎｓｏｆＮｏｎｌｉｎｅａｒＤｏｕｂｌｙＤｅｇｅｎｅｒａｔｅＰａｒａｂｏｌｉｃ...     

Regularity Results for a Strongly Degenerate Parabolic Equation

M. Bertsch & R. Dal Passo proved the existence and uniqueness of the Cauchy problem for u_t = (φ(u),ψ(u_x))_x, where φ > 0, ψ is a strictly increasing function with lim_{s → ∞}ψ(s) = ψ_∞ < ∞. The regularity of the solution has been obtained under the condition φ" < 0 or φ = const. In the present paper, under the condition φ" ≤ 0, we give some regularity results. We show that the solution can be classical after a finite time. Further, under the condition φ" ≤ -α_0 (where -α_0 is a constant), we prove the gradient of the solution converges to zero uniformly with respect to x as t → +∞.     

一类强退化抛物方程弱解的惟一性

研究了如下形式的强退化抛物方程(C)(u)/(t)=(2A(u,x,t))/(x2)+(B(u,x,t))/(x),基于Holm gren方法,证明了弱解的惟一性.     

一类强退化拟线性抛物方程的弱解

In this paper, we show the existence of the renormalized solutions and the entropy solutions of a class of strongly degenerate quasilinear parabolic equations.     

一类拟线性退化抛物方程的Cauchy问题

对方程α（xx）u＋uαyu-αtu=f（·,u）,（x,y,t）∈R^2×（0,T）的Cauchy问题,给出了一个整体BV-弱解的定义,证明了该弱解的连续性.     

具Lp初值的拟线性退化抛物方程的熵解

拟线性退化抛物方程来自于反应扩散等许多物理问题,有着深刻的应用背景．本文利用Young测度的概念和Div- Curl引理证明了在0≤U0(x)∈L2(R)∩Lp(R)和f是真正非线性函数的条件下,存在一Lp熵解．     

Traveling Wave Fronts of a Degenerate Parabolic Equation with Non-divergence Form

We study the traveling wave solutions of a nonlinear degenerate parabolic equation with non-divergence form. Under some conditions on the source, we establish the existence, and then discuss the regularity of such solutions.     

一类退化抛物方程的边值问题

In this paper, we study the boundary value problem (BVP) for a degenerate parabolic equation. By introducing a proper notion of weak solutions, we prove the uniqueness and existence of weak solutions of the problem. The localization of weak solutions is also discussed, which plays a key role in the proof of the uniqueness.     

Nonlinear Degenerate Parabolic Equation with Nonlinear Boundary Condition

In this paper, we obtain the necessary and sufficient conditions on the global existence of all positive （weak） solutions to a nonlinear degenerate parabolic equation with nonlinear boundary condition.     

Source Type Solutions of a Fourth Order Degenerate Parabolic Equation

In this paper, we study a generalized thin film equation which is relevant to capillary driven flows of thin films of power-law fluids. We prove that the generalized thin film equation in dimension d ≥ 2 has a unique C^1 source type radial self-similar nonnegative solution if 0 〈 n 〈 2p - 1 and has no solution of this type if n ≥ 2p - 1.