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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 7 > No. 1


Nonlinear Pedestrian-flow Model: Uniform Wellposedness and Global Existence

PP: 29-40
Christian Dogbe,
This paper is concerned with the existence, uniqueness and propagation of monotonous properties for a certain class of Cauchy problems for first-order Hamilton-Jacobi equations for which initial data is a gradient function. In particular, we show that the monotonicity properties are propagated under certain assumptions. The main result is gained by the method of characteristics and a priori estimates under a monotonicity criterion. Applications of equations studying here refer to control problems in crowd dynamics.

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