Geodesic
Decay results for viscoelastic diffusion equations in absence of instantaneous elasticity
Electronic journal of differential equations, Tome 2012 (2012)
We study the diffusion equation in the absence of instantaneous elasticity

$ u_t-\int_0^{t}g(t-\tau )\Delta u(\tau )\,d\tau =0,\quad (x,t)\in \Omega \times (0,+\infty ), $

where $\Omega \subset \mathbb{R}^n$, subjected to nonlinear boundary conditions. We prove that if the relaxation function g decays exponentially, then the solutions is exponential stable.
Classification : 35B05, 35L05, 35L15, 35L70
Keywords: diffusion equation, instantaneous elasticity, exponential decay, relaxation function, viscoelastic 
@article{EJDE_2012__2012__a67,
     author = {Kafini,  Mohammad},
     title = {Decay results for viscoelastic diffusion equations in absence of instantaneous elasticity},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1254.35232},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a67/}
}
TY  - JOUR
AU  - Kafini,  Mohammad
TI  - Decay results for viscoelastic diffusion equations in absence of instantaneous elasticity
JO  - Electronic journal of differential equations
PY  - 2012
VL  - 2012
UR  - http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a67/
LA  - en
ID  - EJDE_2012__2012__a67
ER  - 
%0 Journal Article
%A Kafini,  Mohammad
%T Decay results for viscoelastic diffusion equations in absence of instantaneous elasticity
%J Electronic journal of differential equations
%D 2012
%V 2012
%U http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a67/
%G en
%F EJDE_2012__2012__a67
Kafini,  Mohammad. Decay results for viscoelastic diffusion equations in absence of instantaneous elasticity. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a67/