This paper is concerned with the evolutionary p-Laplacian with interior and boundary sources.The critical exponents for the nonlinear sources are determined.
In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption ut - △um ＋ yup = 0,where γ≥0,m〉 1and P〉m＋2/N We will show that if γ...In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption ut - △um ＋ yup = 0,where γ≥0,m〉 1and P〉m＋2/N We will show that if γ=0 and 0〈μ〈 2N/n（m-1）＋2 or γ 〉 0 and 1/p-1 〈 μ 〈 2N/N（m-1）＋2 then for any nonnegative function φ in a nonnegative countable subset F of the Schwartz space S（RN）, there exists an initial-value u0 ∈ C（RN） with limx→∞ uo（x）= 0 such that φ is an w-limit point of the rescaled solutions tμ/2u（tβ, t）, Where β = 2-μ（m-1）/4.展开更多
This paper is devoted to viscous Cahn-Hiliiard equation with concentration dependent mobility. Some results on the existence, uniqueness and large time behavior are established.
Consider a nonhomogeneous fluid flowing through a homogeneous porous medium occupyinga bounded domain ΩR^n.Let u=u(x,t)represent the density of the fluid at the positionx∈Ω and time t,which satisfies the following ...Consider a nonhomogeneous fluid flowing through a homogeneous porous medium occupyinga bounded domain ΩR^n.Let u=u(x,t)represent the density of the fluid at the positionx∈Ω and time t,which satisfies the following singular diffusion展开更多
This paper is devoted to a strongly degenerate or singular quasilinear parabolic equation.We first extend Kalashnikov's ekistence results [6] to a general situation for the equation without convexity. As a supplem...This paper is devoted to a strongly degenerate or singular quasilinear parabolic equation.We first extend Kalashnikov's ekistence results [6] to a general situation for the equation without convexity. As a supplementation, we also discuss the regularity and uniqueness of solutions展开更多
Under some conditions, one seows that the generalized solutions of the first boundary value problem for the equation [GRAPHICS] have the property of finite speed of propagation.
基金supported by NSFCResearch Fundfor the Doctoral Program of Higher Education of China,Fundamental Research Project of Jilin University(200903284)Graduate Innovation Fund of Jilin University(20101045)
文摘This paper is concerned with the evolutionary p-Laplacian with interior and boundary sources.The critical exponents for the nonlinear sources are determined.
基金supported by National Natural Science Foundation of Chinasupported by Specialized Research Fund for the Doctoral Program of Higher Educationsupported by Graduate Innovation Fund of Jilin University (20101045)
文摘In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption ut - △um ＋ yup = 0,where γ≥0,m〉 1and P〉m＋2/N We will show that if γ=0 and 0〈μ〈 2N/n（m-1）＋2 or γ 〉 0 and 1/p-1 〈 μ 〈 2N/N（m-1）＋2 then for any nonnegative function φ in a nonnegative countable subset F of the Schwartz space S（RN）, there exists an initial-value u0 ∈ C（RN） with limx→∞ uo（x）= 0 such that φ is an w-limit point of the rescaled solutions tμ/2u（tβ, t）, Where β = 2-μ（m-1）/4.
基金Qutstanding Youth Foundation (10125107) of China a Key Grant of the Ministry of Science and Technologies.
文摘This paper is devoted to viscous Cahn-Hiliiard equation with concentration dependent mobility. Some results on the existence, uniqueness and large time behavior are established.
文摘Consider a nonhomogeneous fluid flowing through a homogeneous porous medium occupyinga bounded domain ΩR^n.Let u=u(x,t)represent the density of the fluid at the positionx∈Ω and time t,which satisfies the following singular diffusion
文摘This paper is devoted to a strongly degenerate or singular quasilinear parabolic equation.We first extend Kalashnikov's ekistence results [6] to a general situation for the equation without convexity. As a supplementation, we also discuss the regularity and uniqueness of solutions
文摘Under some conditions, one seows that the generalized solutions of the first boundary value problem for the equation [GRAPHICS] have the property of finite speed of propagation.
