考虑一类主部为发展型p-Laplace算符的方程组,建立了用于描述这类问题的一个新模型,给出了该方程组弱解的定义,证明了一系列关于弱解的积分估计和单调性估计,并获得了该方程组弱解的存在性和惟一性以及当反应速率趋于无穷时弱解的收敛性.由快速反应模型(反应速率趋于无穷)的形式上可见,所得结果与实际估计一致.
A mathematical model describing the interaction between virus and antibody was studied. The authors modified the origional model first by replacing the Laplacian in the origional model with a nonlinear p-Laplacian operator and then proved the existence and uniqueness of the weak solutions to the model. Also, the authors studied the limit behavior of the solution as the reaction rate tended to infinity. The result obtaind coincides with the case one can observe.