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

Jan Harm van der Walt
2013 Abstract and Applied Analysis  
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.
doi:10.1155/2013/739462 fatcat:uci6i624ybdhhe7pr3pq5u64de