Gradient theory of phase transitions with boundary contact energy (Q1101675)

The author studies the asymptotic behavior, as \(\epsilon\) goes to zero, of solutions of the variational problems for the van der Waals-Cahn- Hilliard theory of phase transitions in a fluid. The internal free energy, per unit volume, is assumed to be given by \(\epsilon^ 2\) times the square of the gradient of the density \(\delta\) plus a function of \(\delta\), and the contact energy with the container walls, per unit surface area, is given by \(\epsilon\) times a function of the density \(\delta\). The result is the asymptotic behavior, as \(\epsilon\) goes to zero, of solutions by looking for a variational problem solved by the limit solution. This limit problem exists and agrees with the so-called liquid-drop problem.