EXISTENCE AND UNIQUENESS OF GLOBAL SOLUTION FOR CERTAIN NONLINEAR DEGENERATE PARABOLIC SYSTEMS

摘要

Our purpose is to prove the existence and uniqueness of locally bounded global solution in Ω x (0,T] for system. The problem with a_i(u_i) ≡ u_i~(m_i) and b_i(x,t,u_i) ≡ 0 has been studied by L. Maddalena in [4]. As a result of using an unsuitable method by the author in [4], the major estimate on L~∞-norm for the solution is a failure. Since we consider the problem with the terms of first derivative and the data u_i~0 as some functions of L~(p_i) (Ω) for p_i > p_i~0 here, we have some substantial difficulties in investigating the result on existence and uniqueness. Because u_i ∈ L~(p_i)(Ω), we get only an interior estimate on L~∞-norm of these solutions of the approximating nondegenerate problem of (1.1)-(1.3). In addition, in tackling the problem with the terms of first order derivative, we must confront the hardship of proving the uniqueness theorem. With an accurate estimate on L~∞-norm of solution u and the boundary estimate on normal derivative for the solution of the adjoint problem, we overcome the difficulties.