Perturbation method of boundary geometry (PMOBG) is used in rectangular waveguides with one-dimension perturbed walls and mode analyses are made.

The inverse method is a combination of the perturbation boundary element method and the Kalman filter.

Singular perturbation for system of Volterra type integral differential equations with boundary perturbation;

Asympotic solution and solvable conditions for a class of nonlinear problem with boundary perturbation;

Semilinear singularly perturbed problem with boundary perturbation;

A nonlinear problem for reaction diffusion equation with a perturbed boundary is considered.

The method of determining OOIP, gas - bearing area, boundary shape, well location and vertical fracture length for the closed isochoric oil reservoirs is proposed using combined solution of the nonsteady state equation and the pseuosteady state equation of pressure drawdown curves.

Regarding the separate boundary shape of elastic structures as random variables, stochastic equations and boundary conditions that govern eigenvalue problems are set up.