The existence and uniqueness of a variational solution are proved for the following nonautonomous nonclassical diffusion equation ut − εΔut − Δu f u g x, t , ε ∈ 0, 1 , in a noncylindrical domain with homogeneous Dirichlet boundary conditions, under the assumption that the spatial domains are bounded and increase with time. Moreover, the nonautonomous dynamical system generated by this class of...

In this paper, we study the asymptotic behavior of solutions to a non-autonomous diffusion equations with delay containing some hereditary characteristics and nonlocal in time-dependent space $$C_{\mathcal {H}_{t}(\varOmega )}$$ . When nonlinear function f satisfies polynomial growth arbitrary order $$p-1$$ $$(p \ge 2)$$ external force $$h \in L_{l o c}^{2}\left( \mathbb {R}; H^{-1}(\varOmega )...

<p style='text-indent:20px;'>In this paper, we investigate a class of stochastic recurrent neural networks with discrete and distributed delays for both biological mathematical interests. We do not assume any Lipschitz condition on the nonlinear term, just continuity assumption together growth conditions so that uniqueness Cauchy problem fails to be true. Moreover, existence pullback attr...