Existence and Uniqueness of Global Solution for Certain Degenerate Reaction-Diffusion Systems

In this paper we discuss the following nonlinear degenerate parabolic systems u_i=△a_i(u_i)+b_i(x,t,u_i)Du_i+f_i(x,t,u)for i = 1,2, …, m and u = (u_1,…, u_m) is a vector function, with Dirichlet boundary condition. Under some structure conditions on a_i,b_i and f_i and initial data u_i^o∈Li(Ω) for some pi>p_i^o = 1,2,…,m, the result on existence and uniquence of global solution is established.

In this paper we discuss the following nonlinear degenerate parabolic systemsut = Δαi(ui) + bi(x,t, ui)Dui+ fi(x,t,u)for i = 1,2,… ,m and u= (u1,…,um) is a vector function, with Dirichlet boundary condition. Under some structure conditions on αi,bi and fi and initial data ui ∈ Li(Ω) for some pi> pi°,i = 1,2,… ,m, the result on existence and uniquence of global solution is established.