Blowup and Asymptotic Behavior of a Free Boundary Problem with a Nonlinear Memory (Journal of Partial Differential Equations, 2020)
In this paper, we investigate a reaction-diffusion equation $u_t-du_{xx}=au+\int_{0}^{t}u^p(x,τ){\rm d}τ+k(x)$ with double free boundaries. We study blowup phenomena in finite time and asymptotic behavior of time-global solutions. Our results show if $\int_{-h_0}^{h_0}k(x)ψ_1 {\rm d}x$ is large enough, then the blowup occurs. Meanwhile we also prove when $T^*