Publicado
Stability of Equilibrium Solutions of a Nonlinear Reaction-Diffusion Equation
Estabilidad de Soluciones de Equilibrio de una Ecuación de Reacción-Difusión no Lineal
Palabras clave:
Reaction-Diffusion equation, equilibrium solutions, stability (en)Ecuación de reacción-difusión, soluciones de equilibrio, estabilidad (es)
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In the present work, it is analyzed existence and stability of equilibrium solutions of the following nonlinear reaction-diusion equation:
ut = auxx + wu + k ln(u2)u.
Explicit formulas for a family of equilibrium solutions to the former equation which decay to zero at innity are provided. The instability of those solutions is obtained by detailed spectral analysis of the linear operator which approximates the solutions of the equation around the equilibrium solutions. A result about the instability of any non-trivial equilibrium solution of the equation is also established.
En el presente trabajo, se analiza la existencia y estabilidad de soluciones de equilibrio de la siguiente ecuación de reacción-difusión no lineal:
ut = auxx + wu + k ln(u2)u.
Se proporcionan fórmulas explícitas para una familia de soluciones de equilibrio de la ecuación anterior que decaen a cero en infinito. La inestabilidad de esas soluciones se obtienen mediante el análisis espectral detallado del operador lineal que aproxima las soluciones de la ecuación alrededor de las soluciones de equilibrio. También se establece un resultado sobre la inestabilidad de cualquier solución de equilibrio no trivial de la ecuacióan.
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