The nonlinear heat equation with state-dependent parameters and its connection to the Burgers' and the potential Burgers' equation

Christoph Josef Backi, Jan Dimon Bendtsen, John Leth, Jan Tommy Gravdahl
2014 IFAC Proceedings Volumes  
In this work the stability properties of a nonlinear partial differential equation (PDE) with state-dependent parameters is investigated. Among other things, the PDE describes freezing of foodstuff, and is closely related to the (Potential) Burgers' Equation. We show that for certain forms of coefficient functions, the PDE converges to a stationary solution given by (fixed) boundary conditions that make physical sense. We illustrate the results with numerical simulations.
doi:10.3182/20140824-6-za-1003.01278 fatcat:bkkrhjer45awjnv4vaddvl36de