In this paper we combine elements of the b-calculus and elliptic boundary problems to solve the decomposition problem for the (regularized) ζ-determinant of the Laplacian on a manifold with cylindrical end into the ζ-determinants of the Laplacians with Dirichlet conditions on the manifold with boundary and on the half infinite cylinder. We also compute all the contributions to this formula expl...

Aerodynamic sound generation at low Mach numbers around complex stationary and moving bodies is computed directly with an immersed-boundary method-based hybrid approach. The complex flow field is solved by the immersed-boundary incompressible Navier-Stokes flow solver and the sound generation and propagation are computed by the linearized perturbed compressible equations with a high-order immer...

We study solution techniques for parabolic equations with fractional diffusion and Caputo fractional time derivative, the latter being discretized and analyzed in a general Hilbert space setting. The spatial fractional diffusion is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem posed on a semi-infinite cylinder in one more spatial dimension. We write our evolution ...

We study a discretization technique for the parabolic fractional obstacle problem in bounded domains. The fractional Laplacian is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic equation posed on a semi-infinite cylinder, which recasts our problem as a quasi-stationary elliptic variational inequality with a dynamic boundary condition. The rapid decay of the solution suggest...

We present a computer assisted proof or diffusion in the Planar Elliptic Restricted Three Body Problem. treat elliptic problem as perturbation of circular problem, where parameter is eccentricity primaries. The unperturbed system preserves energy, and we show that for sufficiently small perturbations have orbits with explicit energy changes, independent from size perturbation. result based on s...

For the characteristics of horizontal fractures in shallow low-permeability oil layers after hydraulic fracturing in multilayer reservoirs, horizontal fractures are taken equivalent to an elliptical cylinder with the reservoir thickness using the equivalent permeability model; then, upon the elliptic seepage theory, the seepage field which has led by a vertical well with horizontal fractures is...