All Questions

I have a general question. Suppose that we have the following simple evolution problem $\begin{cases} \dfrac{\partial u}{\partial t}-\Delta u=f(u), & (t,x)\in (0,\infty)\times\Omega\\ \dfrac{\...

Studying the Fisher-KPP evolution equation I came across the steady state elliptic problem which can be written in the following form: $$ \begin{cases} -d\Delta Y(x)=r(x)Y(x)\left (1-\dfrac{Y(x)}{K(x)}...

I wonder if there is a good reference on reaction-diffusion systems on $\mathbb{R}^N$, that treats them as dynamical systems. I have the books of Alain Haraux – Systèmes dynamiques dissipatifs et ...

Edit: According to the comment of Willie Wong I realize that the previous version was trivial. I thank him for his comment. Now I revise it. We consider the heat equation $$U_{t}=\Delta U\\U(x,y,0)=...