Blow-up behavior of solutions to the heat equation with nonlinear boundary conditions (Q2513305)

Given the heat equation in the half space of \(\mathbb{R}^n\) with nonlinear boundary conditions of the form \(\partial_\nu u=u^q\), the authors study the asymptotic behavior of blow-up solutions near the blow-up time and their blow-up profiles. Here, the blow-up profile of a blow-up solution is the shape attained by the solution when the time tends to the blow-up time.