On a one-phase Stefan problem in nonlinear conduction
S. de Lillo, M. C. Salvatori
TL;DR
This paper investigates a one-phase Stefan problem involving nonlinear conduction, establishing existence of solutions for small times and deriving an exact traveling front solution with constant speed.
Contribution
It provides the first exact traveling front solution for this nonlinear Stefan problem and proves local existence and uniqueness of solutions.
Findings
Unique solution exists for small times
Exact traveling front solution derived
Traveling front moves with constant speed
Abstract
A one phase Stefan problem in nonlinear conduction is considered. The problem is shown to admit a unique solution for small times. An exact solution is obtained which is a travelling front moving with constant speed.
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Taxonomy
TopicsLattice Boltzmann Simulation Studies · Fluid Dynamics and Thin Films · Fluid Dynamics and Heat Transfer