Geodesic
Decay results for viscoelastic diffusion equations in absence of instantaneous elasticity
Electronic journal of differential equations, Tome 2012 (2012)
Zbl
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 
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/
@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/}
}
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