Asymptotic behavior of solutions of a reaction diffusion equation with free boundary conditions

Jingjing Cai, Bendong Lou, Maolin Zhou

We study a nonlinear diffusion equation of the form $u_t=u_{xx}+f(u)(x\in [g(t),h(t)])$ with free boundary conditions $g^{\prime }(t)=-u_x(t,g(t))+\alpha$ and $h^{\prime }(t)=-u_x(t,g(t))-\alpha$ for some $…