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....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.展开更多
In this paper, the initial boundary value problem of semilinear degenerate reaction-diffusion systems is studied. The regularization method and upper and lower solutions technique are employed to show the existence an...In this paper, the initial boundary value problem of semilinear degenerate reaction-diffusion systems is studied. The regularization method and upper and lower solutions technique are employed to show the existence and continuation of a positive classical solution. The location of quenching points is found. The critical length is estimated by the eigenvalue method.展开更多
基金Research supported by the Natural Science Foundation of Fujian Province Under Grant A92025.
文摘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.
文摘In this paper, the initial boundary value problem of semilinear degenerate reaction-diffusion systems is studied. The regularization method and upper and lower solutions technique are employed to show the existence and continuation of a positive classical solution. The location of quenching points is found. The critical length is estimated by the eigenvalue method.
