We study positive solutions y(u) to 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 on [0,1] such that f(0)=0=f(1). We shall be particularly concerned with 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 spacial 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.

A class of singular first order differential equations with applications in reaction-diffusion / Enguiça, Ricardo; Gavioli, Andrea; Sanchez, Luis. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B. - ISSN 1553-524X. - STAMPA. - 33:1(2013), pp. 173-191. [10.3934/dcds.2013.33.173]

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

GAVIOLI, Andrea;
2013

Abstract

We study positive solutions y(u) to 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 on [0,1] such that f(0)=0=f(1). We shall be particularly concerned with 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 spacial 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.
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A class of singular first order differential equations with applications in reaction-diffusion / Enguiça, Ricardo; Gavioli, Andrea; Sanchez, Luis. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B. - ISSN 1553-524X. - STAMPA. - 33:1(2013), pp. 173-191. [10.3934/dcds.2013.33.173]
Enguiça, Ricardo; Gavioli, Andrea; Sanchez, Luis
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/817700
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