In this paper, we consider the problem (θ(x,U))_t=(K(x,U)U_x)_x-(K(x,U))_x (x,t)∈G_T (θ(x,U)V(x,t))_t=(DθV_x)_x+(V(KU_x-K))_x,(x,t)∈G_T, u(x,0)=u_0(x),V(x,0),(x,0)=V_0(x),0≤x≤2, U(0,t)=h_0(t),U(2,t)=h_2(t),0≤t≤T, V(0,t)=g_0(t),V(2,t)=g_2(t),0≤t≤T. Where, θ(x,U)=θ_1(x,U) when (x,t)∈D_1={0≤x<1,0≤t≤T};θ(x,U)=θ_2(x,U),(x,t)∈D_2={1
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.
