The 3D Happel model for complete isotropic Stokes flow.
The asymptotic behaviour of surfaces with prescribed mean curvature near meeting points of fixed and free boundaries
We study the shape of stationary surfaces with prescribed mean curvature in the Euclidean 3-space near boundary points where Plateau boundaries meet free boundaries. In deriving asymptotic expansions at such points, we generalize known results about minimal surfaces due to G. Dziuk. The main difficulties arise from the fact that, contrary to minimal surfaces, surfaces with prescribed mean curvature do not meet the support manifold perpendicularly along their free boundary, in general.
The Calderón Projector for an Elliptic Operator in Divergence Form.
The complex reflection method for some classes of equations with the third derivative distinguished.
The Convergence of Even Degree Spline Collocation Solution for Potential Problems in Smooth Domains of the Plane.
The decomposition method for linear, one-dimensional, time-dependent partial differential equations.
The different solutions of the partial differential equations and the comparing of them
The effect of thin coatings on second harmonic generation.
The evolution of dust emitted by a uniform source above ground level.
The existence of nonclassical asymptotic expansion of the trace of a heat kernel for a degenerate elliptic operator.
The extended tanh-mehtod for finding traveling wave solutions of nonlinear evolution equations.
The Feynman-Kac formula for a system of parabolic equations
The Fourier method for the linear partial differential equations of the -th order
The general method for solving the partial differential equation of any order with unknown function depending on any number of arguments and the system of such equations
The generalized Airy diffusion equation.
The Green Function for Uniformly Elliptic Equations.
The interface crack with Coulomb friction between two bonded dissimilar elastic media
We study a model of interfacial crack between two bonded dissimilar linearized elastic media. The Coulomb friction law and non-penetration condition are assumed to hold on the whole crack surface. We define a weak formulation of the problem in the primal form and get the equivalent primal-dual formulation. Then we state the existence theorem of the solution. Further, by means of Goursat-Kolosov-Muskhelishvili stress functions we derive convergent expansions of the solution near the crack tip.
The jump problem for mixed-type equations with defects on the type change line.
The Laplace method of the linear partial differential equations of the -th order
The level crossing problem in semi-classical analysis I. The symmetric case
We describe a microlocal normal form for a symmetric system of pseudo-differential equations whose principal symbol is a real symmetric matrix with a generic crossing of eigenvalues. We use it in order to give a precise description of the microlocal solutions.