Sentence examples for singular coefficient from inspiring English sources

We study the limit of the solution of linear and semilinear second order PDEs of parabolic type, with rapidly oscillating periodic coefficients, singular drift, and singular coefficient of the zeroth order term.

We do not impose any restrictions on the growth or the sign of the singular coefficient.

Such a singular coefficient matrix does not occur for j = 2, so this will be our choice.

The interest of this algorithm is the approximation of the solution and the leading singular coefficient which has a physical significance in the propagation of cracks.

The consideration of using off-step nodal points for discretization is motivated by the polar form of one space Laplacian operator (nabla ^{2}equivpartial^{2}/partial r^{2}+(alpartial/partialpartial r)), which has a singular coefficient associated with the first-order derivative term.

(5) The regular part of the solution ({tilde{varphi}}_{R}) is in the space (H^{s+2}(Omega)) such that Vert {tilde{varphi}}_{R} Vert _{H^{s+2}(Omega)}+ vert lambda_{1} vert + vert lambda_{2} vert le C Vert f Vert _{H^{s-2}(Omega)}, where C is a positive constant and (lambda_{2}) is the second singular coefficient.

The proposed method eliminates the need for high-order integration, improves the overall accuracy, and yields very accurate estimates for the singular coefficients.

In this paper we introduce a new technique to construct unique strong solutions of SDE's with singular coefficients driven by certain Lévy processes.

The utility of the variational composition is demonstrated by applications to subdifferential calculus, theory of measurable multifunctions, and elliptic PDEs with singular coefficients.

We also discuss the application of the proposed method to a wave equation with singular coefficients.

In this article, fractional integro-differential inequalities with singular coefficients have been considered.