The Perturbation of the Interface of the Two-dimensional Diffraction Problem and an Approximating Muskat Modal (Journal of Partial Differential Equations, 1990)
ln this paper, a new transformation is found out to straighten the interface &#915_2 x = f(y), f &#8712 C^{2+a}([0, a]), f_y|_y =0, &#948 < f < l-&#948,&#948 > 0,&#948,l=constants and a perturbation of the interface is considered for a two dimensional diffraction problem. And the existence, uniqueness and regularity of an appeoximating Muskat model are proved.