Geodesic
Decay results for viscoelastic diffusion equations in absence of instantaneous elasticity
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Kafini, Mohammad},
     title = {Decay results for viscoelastic diffusion equations in absence of instantaneous elasticity},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a67/}
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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/