Regulation of Viable and Optimal Cohorts

Aubin, Jean‐Pierre

doi:10.1007/s00245-014-9277-x

Cited by 2 publications

(1 citation statement)

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“…In the concrete examples of nonlocal balance laws here, the curves are L p bounded, weakly continuous weak solutions and narrowly continuous distributional solutions with values in the space of signed Radon measures, respectively. These connections to partial differential equations specify essential differences of our results from recent contributions of Aubin et al to traffic flow modelling (see, e.g., [12][13][14]). …”

Section: Mutational Analysis On Spaces Without a Linear Structurementioning

confidence: 63%

Nonlocal multi-scale traffic flow models: analysis beyond vector spaces

Kloeden

Lorenz

2016

Bull. Math. Sci.

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Realistic models of traffic flow are nonlinear and involve nonlocal effects in balance laws. Flow characteristics of different types of vehicles, such as cars and trucks, need to be described differently. Two alternatives are used here, L p -valued Lebesgue measurable density functions and signed Radon measures. The resulting solution spaces are metric spaces that do not have a linear structure, so the usual convenient methods of functional analysis are no longer applicable. Instead ideas from mutational analysis will be used, in particular the method of Euler compactness will be applied to establish the well-posedness of the nonlocal balance laws. This involves the concatenation of solutions of piecewise linear systems on successive time subintervals obtained by freezing the nonlinear nonlocal coefficients to their values at the start of each subinterval. Various compactness criteria lead to a convergent subsequence. Careful estimates of the linear systems are needed to implement this program.

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Section: Mutational Analysis On Spaces Without a Linear Structurementioning

confidence: 63%