Global existence and decay estimates for the semilinear nonclassical-diffusion equations with memory in Rn
M. Berbiche, A. Melik
In this paper, we study the initial value problem for a semi-linear
nonclassical diffusion equations with fading memory in Rn.
Under smallness conditions on the initial data, the global existence and
decay estimates of the solutions are established. Furthermore, time decay
estimates in higher Sobolev space of the solution are provided. The proof is
carried out by means of the pointwise decay estimates of the solution in the
Fourier space and a fixed point-contraction mapping argument.
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