We are concerned with the uniqueness of solutions of the Cauchy problemand a(s),b(s) are appropriately smooth.Since a(s) is allowed to have zero points, we call them points of degeneracy of (1), the equation (1) does ...We are concerned with the uniqueness of solutions of the Cauchy problemand a(s),b(s) are appropriately smooth.Since a(s) is allowed to have zero points, we call them points of degeneracy of (1), the equation (1) does not admit classical solutions in general. The solutions of (1) even might be discontinuous, whenever the set E = {s : a(s) = 0} includes interior points.Equations with degeneracy arise from a wide variety of diffusive processes in nature展开更多
In this paper, we prove some properties of solutions to a class of degener-ate diffusion systems which arise from modeling interacting evolution of two biological groups.
In this paper, we study the existence and nonuniqueness of weak solutions of the initial and boundary value problem for ut= uσdiv(|△u|p-2△u) with σ≥1. Localization property of weak solutions is also discussed.
In this paper, we show the existence of the time periodic solutions to the porous medium equations of the formut= Δ (|u| m-1 u)+B(x,t,u)+f(x,t) in Ω×Rwith the Dirichlet boundary value condition, wher...In this paper, we show the existence of the time periodic solutions to the porous medium equations of the formut= Δ (|u| m-1 u)+B(x,t,u)+f(x,t) in Ω×Rwith the Dirichlet boundary value condition, where m>1, Ω is a bounded domain in R N with smooth boundary Ω , the continuous function f and the Hlder continuous function B(x,t,u) are periodic in t with period ω and the nonlinear sources are assumed to be weaker, i.e., B(x,t,u) u≤b 0|u| α+1 with constants b 0≥0 and 0≤α<m.展开更多
This paper is devoted to the time periodic solutions to the degenerate parabolic equations of the form under the Dirichlet boundary value condition, where m＞1, p≥0, Ω■RN is a bounded domain with smooth boundary б...This paper is devoted to the time periodic solutions to the degenerate parabolic equations of the form under the Dirichlet boundary value condition, where m＞1, p≥0, Ω■RN is a bounded domain with smooth boundary бΩ and a,b are positive, smooth functions which are periodic in t with period ω>0. The existence of nontrivial nonnegative solutions is established provided that 0≤p<m. The existence is also proved in the case p=m but with an additional assumption man a(x,t)>λ1, Q where Al is the first eigenvalue of the operator -△ under the homogeneous Dirichlet boundary condition.展开更多
基金Partially supported by NSF (19631050) of China, partially supported by the grant of Ministry of Science and Technologies of China, and partially supported by the Outstanding Young Fundation (19125107) of China.
文摘We are concerned with the uniqueness of solutions of the Cauchy problemand a(s),b(s) are appropriately smooth.Since a(s) is allowed to have zero points, we call them points of degeneracy of (1), the equation (1) does not admit classical solutions in general. The solutions of (1) even might be discontinuous, whenever the set E = {s : a(s) = 0} includes interior points.Equations with degeneracy arise from a wide variety of diffusive processes in nature
文摘In this paper, we prove some properties of solutions to a class of degener-ate diffusion systems which arise from modeling interacting evolution of two biological groups.
基金The Young Teachers Foundation (420010302318) of Jilin University.
文摘In this paper, we study the existence and nonuniqueness of weak solutions of the initial and boundary value problem for ut= uσdiv(|△u|p-2△u) with σ≥1. Localization property of weak solutions is also discussed.
文摘In this paper, we show the existence of the time periodic solutions to the porous medium equations of the formut= Δ (|u| m-1 u)+B(x,t,u)+f(x,t) in Ω×Rwith the Dirichlet boundary value condition, where m>1, Ω is a bounded domain in R N with smooth boundary Ω , the continuous function f and the Hlder continuous function B(x,t,u) are periodic in t with period ω and the nonlinear sources are assumed to be weaker, i.e., B(x,t,u) u≤b 0|u| α+1 with constants b 0≥0 and 0≤α<m.
基金the National Natural Sciences Foundation of Chinathe project of Differential Equation and Application.
文摘This paper is devoted to the time periodic solutions to the degenerate parabolic equations of the form under the Dirichlet boundary value condition, where m＞1, p≥0, Ω■RN is a bounded domain with smooth boundary бΩ and a,b are positive, smooth functions which are periodic in t with period ω>0. The existence of nontrivial nonnegative solutions is established provided that 0≤p<m. The existence is also proved in the case p=m but with an additional assumption man a(x,t)>λ1, Q where Al is the first eigenvalue of the operator -△ under the homogeneous Dirichlet boundary condition.
