I would like to know if it is true that the solution of the equation $\partial_tu(x,t)=\Delta u(x,t)+f(x) ,t\ge0, u=0 $ for $x\in R^n , t=0$ converges to the solution of $\Delta u=-f, x\in R^n$ as $t\to \infty$ ? How can i show if its true ?
What i am thinking is to use duhamels principle and find the solution and what should i do next ?
Thank you for your help .