Existence, uniqueness and stability of weak solutions of parabolic systems with discontinuous nonlinearities
The paper is devoted to the initial value problem for parabolic systems with discontinuous nonlinearities. First, the authors proof the existence of the maximal or minimal weak solution of the problem in an order interval, by using the upper and lower solution method combined with the monotone iterative technique. Due to the discontinuous nonlinearities, there is no uniqueness of weak solutions of the considered problem for general initial data. This fact is illustrated with an example. Then, the authors prove that certain classes of initial data guarantee the global uniqueness of weak solutions with \(n=2\). In the ending, the authors study the stability of two constant stationary solutions \textbf{0} and \textbf{1}.
scientific article; zbMATH DE number 5553488
scientific article