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 → ∞. 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.
| Original language | English |
|---|---|
| Pages (from-to) | 271-292 |
| Number of pages | 22 |
| Journal | Tokyo Journal of Mathematics |
| Volume | 39 |
| Issue number | 1 |
| Publication status | Published - 2016 Jun 1 |
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Keywords
- Advection
- Global attractivity
- Logistic equation
- Lyapunov functional
- Spatial inhomogeneity
- Volterra diffusion equation
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Asymptotic behavior of solutions for semilinear volterra diffusion equations with spatial inhomogeneity and advection. / Yoshida, Yusuke; Yamada, Yoshio.
In: Tokyo Journal of Mathematics, Vol. 39, No. 1, 01.06.2016, p. 271-292.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Asymptotic behavior of solutions for semilinear volterra diffusion equations with spatial inhomogeneity and advection
AU - Yoshida, Yusuke
AU - Yamada, Yoshio
PY - 2016/6/1
Y1 - 2016/6/1
N2 - 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 → ∞. 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.
AB - 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 → ∞. 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.
KW - Advection
KW - Global attractivity
KW - Logistic equation
KW - Lyapunov functional
KW - Spatial inhomogeneity
KW - Volterra diffusion equation
UR - http://www.scopus.com/inward/record.url?scp=84983661497&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84983661497&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:84983661497
VL - 39
SP - 271
EP - 292
JO - Tokyo Journal of Mathematics
JF - Tokyo Journal of Mathematics
SN - 0387-3870
IS - 1
ER -