Research Article The Order Completion Method for Systems of Nonlinear PDEs: Solutions of Initial Value Problems

License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We present an existence result for generalized solutions of initial value problems obtained through the order completion method. The solutions we obtain satisfy the initial condition in a suitable extended sense, and each such solution may be represented in a canonical way through its generalized partial derivatives as nearly finite normal lower semicontinuous function. 1