Abstract: We consider the 1D transport equation with nonlocal velocity field: ? t + u ? x + ? ? ? ? = 0 , u = N ( ? ) , where N is a nonlocal operator and ? ? is a Fourier multiplier defined by ? ? ? f ( ? ) = | ? | ? ? f ( ? ) . In this paper, we show the existence of solutions of this model locally and globally in time for various types of nonlocal operators.

Autoría

Descargar referencia