hi while reading article of T. CAZENAVE – F. DICKSTEIN – M. ESCOBED :A semilinear heat equation with concave-convex nonlinearity ,there issomepoints which are not not clear for me:
- is this equation seminear or non linear :
because some times he says that is semilinear and sometimes nonlinear?
- he supposes that there is a function $u_{\alpha}$ which verify $(1.1)$ with initial data $u_{\alpha}(0)$ converging to $u_{0}$ and then he says that we deduce $u_{\alpha}$ converge to u so how can one prove that ? i know that by comparaison principle we have only : $u_{\alpha}\le u$ thanks