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
基金Supported by National Natural Science Foundation of China(11001221)Mathematical Tianyuan Foundation of China(11126027)Northwestern Polytechnical University Jichu Yanjiu Jijin Tansuo Xiangmu(JC201124)
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.
