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Travelling fronts for multidimensional nonlinear transport equations. (English) Zbl 0965.45012
The author considers a nonlinear transport equation as a hyperbolic generalization of the well-known reaction-diffusion equation. The existence of strictly monotone travelling fronts for the three main types of the nonlinearity: the positive source term, the combustion law, and the bistable case is considered. In the first case, there is a whole interval of possible speeds containing its strictly positive minimum. For subtangential nonlinearities an explicit expression for the minimal wave speed is given.

MSC:
45K05 Integro-partial differential equations
45G10 Other nonlinear integral equations
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