| Abstract: |
| In this talk we preset some stability results of semi-wavefronts to the equation $u_t(t, x)=u_{xx}(t, x)+f(u(t, x), u(t-h, x)), \quad t>0, x\in\R$ where $h>0$ is a delay. Unlike non delayed case, we show that the generated solution by an initial datum which is similar to a semi-wavefront $\phi_c(\cdot)$ at time $t=0$ will converge to $\phi_c(x\cdot+ct+a)$, as $t\to+\infty$, where the phase $a\in\R$ is not equal to zero when $f(u, v)=-u+g(v)$. |
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