Edagardo Álvarez

Logarithmic Bramson correction for Fisher--KPP equations on homogeneous trees

In this paper, we study the Fisher--KPP equation \[ \partial_t u = \alpha\Delta_{\TT_{q+1}}u+\beta u(1-u), \] on the homogeneous \((q+1)\)-regular tree \(\TT_{q+1}\), with \(q\geq2\), for nontrivial, compactly supported radial initial data. We first obtain an explicit representation of the fundamental solution of the c...