## Tokyo Journal of Mathematics

### Asymptotic Behavior of Solutions for Semilinear Volterra Diffusion Equations with Spatial Inhomogeneity and Advection

#### Abstract

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.

#### Article information

Source
Tokyo J. Math., Volume 39, Number 1 (2016), 271-292.

Dates
First available in Project Euclid: 30 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1459367268

Digital Object Identifier
doi:10.3836/tjm/1459367268

Mathematical Reviews number (MathSciNet)
MR3543143

Zentralblatt MATH identifier
1350.35034

#### Citation

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

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