In this paper,we consider the degenerate diffusion problem where Ω R^N is an open bounded domain with lipschta boundary Ω9. ψ(u) ∈ c^2[0,∞) ,ψ(s)>O,ψ′(s) >0, ψ′(s)≥0 ,whens>0;ψ(0)= 0,ψ′(0))≥ 0....In this paper,we consider the degenerate diffusion problem where Ω R^N is an open bounded domain with lipschta boundary Ω9. ψ(u) ∈ c^2[0,∞) ,ψ(s)>O,ψ′(s) >0, ψ′(s)≥0 ,whens>0;ψ(0)= 0,ψ′(0))≥ 0. u_0(x)∈ H_0~1(Ω) ∩ C^o(),u_o(x)≥0.g(s) is locally lipschitz continuous on [0,∞), g(0)=0. There exist a constant K,K> maxu_o(x), such that g(K) <0. |g(s)|/ψ(s)≤ M_o when 0≤s≤K ,where M_0 is a constant. We prove the existence and localization phenomena of weak solution of above problem. Under some additional conditions,we prove th uniqueness,contiouous and asymptotic behavier of weak solution.展开更多
Some new properties of polarizable Carnot group are given.By choosing a proper constant a nontrivial solution of a class of non-divergence Dirichlet problem on the polarizable Carnot group is constructed.Thus the mult...Some new properties of polarizable Carnot group are given.By choosing a proper constant a nontrivial solution of a class of non-divergence Dirichlet problem on the polarizable Carnot group is constructed.Thus the multi-solution property of corresponding non-homogeneous Dirichlet problem is proved and the best possible of LQ norm in the famous Alexandrov-Bakelman-Pucci type estimate is discussed.展开更多
In this paper, we consider the Cauchy problem of degenerate parabolic equation not in divergence form u, = uPAu ＋ uq, p 〉 1, q 〉 1, and give the blow-up conditions and the critical Fujita exponents for the existenc...In this paper, we consider the Cauchy problem of degenerate parabolic equation not in divergence form u, = uPAu ＋ uq, p 〉 1, q 〉 1, and give the blow-up conditions and the critical Fujita exponents for the existence of global and non-global solutions to the Cauchy problem.展开更多
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 reguarity of such solutions.
文摘In this paper,we consider the degenerate diffusion problem where Ω R^N is an open bounded domain with lipschta boundary Ω9. ψ(u) ∈ c^2[0,∞) ,ψ(s)>O,ψ′(s) >0, ψ′(s)≥0 ,whens>0;ψ(0)= 0,ψ′(0))≥ 0. u_0(x)∈ H_0~1(Ω) ∩ C^o(),u_o(x)≥0.g(s) is locally lipschitz continuous on [0,∞), g(0)=0. There exist a constant K,K> maxu_o(x), such that g(K) <0. |g(s)|/ψ(s)≤ M_o when 0≤s≤K ,where M_0 is a constant. We prove the existence and localization phenomena of weak solution of above problem. Under some additional conditions,we prove th uniqueness,contiouous and asymptotic behavier of weak solution.
文摘Some new properties of polarizable Carnot group are given.By choosing a proper constant a nontrivial solution of a class of non-divergence Dirichlet problem on the polarizable Carnot group is constructed.Thus the multi-solution property of corresponding non-homogeneous Dirichlet problem is proved and the best possible of LQ norm in the famous Alexandrov-Bakelman-Pucci type estimate is discussed.
文摘In this paper, we consider the Cauchy problem of degenerate parabolic equation not in divergence form u, = uPAu ＋ uq, p 〉 1, q 〉 1, and give the blow-up conditions and the critical Fujita exponents for the existence of global and non-global solutions to the Cauchy problem.
文摘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 reguarity of such solutions.
