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.
"The Order Completion Method for Systems of Nonlinear PDEs: Solutions of Initial Value Problems." Abstr. Appl. Anal. 2013 1 - 12, 2013. https://doi.org/10.1155/2013/739462