A class of singular first order differential equations with applications in  reaction-diffusion

Enguiça, Ricardo Roque; Gavioli, Andrea; Sanchez, Luis

http://hdl.handle.net/10400.21/3812

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Authors

Enguiça, Ricardo Roque

Gavioli, Andrea

Sanchez, Luis

Abstract(s)

We study positive solutions y(u) for the first order differential equation y' = q(cy(1/p) - f(u)) where c > 0 is a parameter, p > 1 and q > 1 are conjugate numbers and f is a continuous function in [0, 1] such that f(0) = 0 = f(1). We shall be particularly concerned with positive solutions y(u) such that y(0) = 0 = y(1). Our motivation lies in the fact that this problem provides a model for the existence of travelling wave solutions for analogues of the FKPP equation in one space dimension, where diffusion is represented by the p-Laplacian operator. We obtain a theory of admissible velocities and some other features that generalize classical and recent results, established for p = 2.

Description

Agências Financiadoras: FCT e MIUR

Keywords

p-Laplacian FKPP equation Heteroclinic Travelling wave Critical speed Sharp solution

URI

http://hdl.handle.net/10400.21/3812

Citation

ENGUIÇA, Ricardo; GAVIOLI, Andrea; SANCHEZ, Luis - A class of singular first order differential equations with applications in reaction-diffusion. Discrete and Continuous Dynamical Systems. Vol. 33, nr. 1 (2013), p. 173-191.