Tokyo Journal of Mathematics
- Tokyo J. Math.
- Volume 39, Number 1 (2016), 271-292.
Asymptotic Behavior of Solutions for Semilinear Volterra Diffusion Equations with Spatial Inhomogeneity and Advection
This paper is concerned with semilinear Volterra diffusion equations with spatial inhomogeneity and advection. We intend to study the effects of interaction among diffusion, advection and Volterra integral under spatially inhomogeneous environments. Since the existence and uniqueness result of global-in-time solutions can be proved in the standard manner, our main interest is to study their asymptotic behavior as $t\to \infty$. For this purpose, we study the related stationary problem by the monotone method and establish some sufficient conditions on the existence of a unique positive solution. Its global attractivity is also studied with use of a suitable Lyapunov functional.
Tokyo J. Math., Volume 39, Number 1 (2016), 271-292.
First available in Project Euclid: 30 March 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35B40: Asymptotic behavior of solutions
Secondary: 35J61: Semilinear elliptic equations 35K57: Reaction-diffusion equations 35R09: Integro-partial differential equations [See also 45Kxx] 92D25: Population dynamics (general)
YOSHIDA, Yusuke; YAMADA, Yoshio. Asymptotic Behavior of Solutions for Semilinear Volterra Diffusion Equations with Spatial Inhomogeneity and Advection. Tokyo J. Math. 39 (2016), no. 1, 271--292. doi:10.3836/tjm/1459367268. https://projecteuclid.org/euclid.tjm/1459367268