Dynamics of Partial Differential Equations
Volume 10 (2013)
Existence, uniqueness and asymptotic behavior of solutions for a nonclassical diffusion equation with delay
Pages: 267 – 281
A nonclassical nonautonomous diffusion equation with delay is analyzed. First, we prove the existence and uniqueness of solutions by using the Galerkin approximations and the energy method. Next, we prove the existence and eventual uniqueness of stationary solutions, as well as their exponential stability. We emphasize that the assumptions imposed on the delay term include, in particular, the case of measurable variable delays.
diffusion equation with delay, existence and uniqueness
2010 Mathematics Subject Classification