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


Autoria(s): Enguiça, Ricardo Roque; Gavioli, Andrea; Sanchez, Luis
Data(s)

16/09/2014

16/09/2014

01/01/2013

Resumo

Agências Financiadoras: FCT e MIUR

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.

Identificador

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.

1078-0947

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

10.3934/dcds.2013.33.173

Idioma(s)

eng

Publicador

Amer Inst Mathematical Sciences

Relação

SI

https://www.aimsciences.org/journals/displayArticles.jsp?paperID=7607

Direitos

restrictedAccess

Palavras-Chave #p-Laplacian #FKPP equation #Heteroclinic #Travelling wave #Critical speed #Sharp solution
Tipo

article