Radial Symmetry of Self-Similar Solutions for Semilinear Heat Equations

A Variational Approach to Self-Similar Solutions for Semilinear Heat Equations

“…By the uniqueness result [19], we find that w 0 defined by (9) coincides with the non-unique solution of (4) constructed by [13].…”

On Gaussian decay estimates of solutions to some linear elliptic equations and their applications

“…On the other hand, in [4] they also proved that there are no solutions to (1.32) [18] proved that when n ≥ 2 if a solution u is positive and satisfies (1.33) then it must be radially symmetric. As for the case of n = 1, any positive and rapidly decreasing solution must be even symmetric with respect to the origin by [15].…”

“…However, when the solution u ∈ L 2 G is positive it is already known by [18] that u must be radially symmetric, and thus, the asymptotics (1.37) is already established by [21].…”

An evolutionary weighted $p$-Laplacian with Neumann boundary value condition in a perforated domain

“…The main interest lies in the study of the asymptotic behavior of solutions when the radii of the small balls shrink to one point. From those works, see [13]- [17], a very important method in studying the properties of the solutions is firstly to discuss the radially symmetric steady solutions, which can be regarded as a special class of the problems in perforated domains.…”