Sentence examples for boundary for the solution from inspiring English sources

Kohn's work, which should be viewed as the starting point for the Hodge Theorem on manifolds with boundary, provided (L^2) estimates and regularity up to the boundary for the solution of the Cauchy Riemann equations having minimal (L^2) norm.

Preconditioned characteristic boundary conditions (BCs) are implemented at artificial boundaries for the solution of the two- and three-dimensional preconditioned Euler equations at low Mach number flows.

The preconditioned characteristic boundary conditions based on the artificial compressibility (AC) method are implemented at artificial boundaries for the solution of two- and three-dimensional incompressible viscous flows in the generalized curvilinear coordinates.

Therefore, they correspond to the heat flux (u_{x}(0,t)) at the boundary (x=0) for the solution u of Problem P given in (34).

Quantum mechanical description of the nanopores in semiconductor is given based on the application of even mirror boundary conditions for the solution of the Schrödinger equation; the results of calculations give a reasonable explanation of the experimental data.

It was found that there is a concentration boundary for the original solution: below the boundary, the freeze-dried iPS samples are poorly crystallized but the chains are in a highly ordered 31 helix state; above the concentration boundary, the freeze-dried iPS is in a completely disordered amorphous state.

Finally, we prove Harnack inequality up to the boundary for the positive solutions of the problem ut= Δu+14udist2 x,∂Ω) and we prove heat kernel estimates for small times.

We prove the positivity and continuity up to the boundary for the weak solutions.

The previously developed exact solutions to the heat and mass transfer equations for the gas phase surrounding a spheroidal droplet have been used as boundary conditions for the solutions to these equations in the liquid phase.

In particular, the algorithm, which uses the boundary conditions for the solutions inside the computational domain of the test cases, is available for solving both parabolic and hyperbolic systems of partial differential equations.

A boundary element formulation for the solution of multiple moving boundary problems is presented and tested herein.