The well-posedness of a free boundary problem for Burgers' equation

A General Approach to Stability in Free Boundary Problems

“…Therefore the solution of (4.21) with n=0 and + 0 cannot have a sign change before z=b. Since It remains to show that + (2) 1 is negative and this is more involved. From here on let n=2.…”

The Stefan problem with moving boundary

“…For this, we introduce an appropriate external force f (x, t) sufficiently regular on the right-hand side of the original Problem (1). Therefore, the exact solution is known for suitable choice of f (x, t), which allow us to get the numerical simulation for Problem (1) or Problem (3). The error estimates, in the semi-discrete or fully discrete, can be found [10].…”

“…Flame propagation problems have been established in [2] that studied a mathematical formulation suitable in the analyze for the theory of diffusion flames. Studies the mathematical model of moving ends arising in combustion theory was developed by Schmidt-Lainé [1] and [3]. The discharge or absorption of thermal energy during the change in atom arrangement have been studied in [8] and [7].…”

Analysis of a one-dimensional free boundary flow problem

“…The velocity is assumed to satisfy the viscous Burgers equation on the free space interval, while the position of the free extremity is determined by an ordinary differential equation depending on u. Similar problems have already been treated from the theoretical point of view in the literature, for instance for an Arbitrary-Lagrangian-Eulerian formulation in [5], for a two-fluids problem in [1] or for a given moving boundary in [2].…”