Abstract: Using the corresponding characteristic equations (system of ODEs) of the first order quasilinear  partial differential equations (PDEs), we proved the existence and uniqueness of solutions for the first order quasilinear PDEs with the distributional HenstockKurzweil integral. Finally, we demonstrated that the result was more extensive by examples.

Key words: first order quasilinear partial differential equations (PDEs), derivative of distribution, distributional HenstockKurzweil integral