4 papers
Beyond real blow-up: Masuda detours and complex holonomy
Bernold Fiedler
For real , consider quadratic heat equations like \begin{equation*} \mathbf{w}_t=\mathbf{w}_{\boldsymbolξ\boldsymbolξ} + \mathbf{b}(\boldsymbolξ)\,\mathbf{w}^2 \end{…
Transient rebellions in the Kuramoto oscillator: Morse-Smale structural stability and connection graphs of finite 2-shift type
Jia-Yuan Dai, Bernold Fiedler, Alejandro López-Nieto
The celebrated 1975 Kuramoto model of identical oscillators with phase angle vector and all-to-all coupling reads \beg…
Real-time blow-up and connection graphs of rational vector fields on the Riemann sphere
Bernold Fiedler
Inspired by pioneering work of Kyûya Masuda in the 1980s, only much more recent PDE studies address global boundedness versus finite-time blow-up in complex time. The two phenomen…
Real eternal PDE solutions are not complex entire: a quadratic parabolic example
Bernold Fiedler, Hannes Stuke
In parabolic or hyperbolic PDEs, solutions which remain uniformly bounded for all real times are often called PDE entire or eternal. For example, consider the qu…