A recently proposed model of the enhancement of lava flows is reinterpreted as a kinematic wave theory for the depth of the flow. With this interpretation the longitudinal profile of an advancing flow is considered to be a propagating waveform with its length limited continuously by the amount of lava extruded. The application of kinematic wave formalism provides new insights into the effects of time-dependent source behavior on the shape and extent of the wave. Eruption behavior with a period of increasing flow depth at the source is shown to produce so-called ''breaking points'' in the depth profile where the kinematic wave model itself could be invalid. Two models of such eruption behavior are investigated, and this is shown not to be the case. Specifically, when the conservation of lava volume is imposed, the breaking points always reside beyond the front of the wave. In general, it is found that source behavior propagates downstream faster than the flow advances. Thus only a fraction of the source time dependence is reflected in the shape of the kinematic wave. The remainder of the time-dependent source effects must be deposited in the flow front, lateral margins, or solidifying crust or be dissipated irretrievably by processes not included in the model. The fraction of eruption history contained in the advancing waveform depends crucially on the nature of the flow rate/flow depth relation for the lava. Distal surface waves, budding at the nose of the flow, distal levee collapse, and other volcanological observations may be manifestations of time-dependent source behavior that advanced beyond the kinematic wave front. ¿ American Geophysical Union 1987