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230,139
The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
 SIAM J. Num. Anal
, 1994
"... Abstract. The authors develop finite difference methods for elliptic equations of the form V. ((x)Vu(x)) + (x)u(x) f(x) in a region in one or two space dimensions. It is assumed that gt is a simple region (e.g., a rectangle) and that a uniform rectangular grid is used. The situation is studied in wh ..."
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Cited by 266 (31 self)
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in which there is an irregular surface F of codimension contained in fl across which, a, and f may be discontinuous, and along which the source f may have a delta function singularity. As a result, derivatives of the solution u may be discontinuous across F. The specification of a jump discontinuity in u
for scalar conservation laws with singular sources
 Meth. Appl. Anal
, 2002
"... Abstract. We consider scalar conservation laws with nonlinear singular sources with a concentration effect at the origin. We assume that the flux A is not degenerated and we study whether it is possible to define a wellposed limit problem. We prove that when A is strictly monotonic then the limit p ..."
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Cited by 6 (0 self)
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Abstract. We consider scalar conservation laws with nonlinear singular sources with a concentration effect at the origin. We assume that the flux A is not degenerated and we study whether it is possible to define a wellposed limit problem. We prove that when A is strictly monotonic then the limit
Singular sources mining using evidential conflict analysis
, 2012
"... Singular sources mining is essential in many applications like sensor fusion or dataset analysis. A singular source of information provides pieces of evidence that are significantly different from the majority of the other sources. In the DempsterShafer theory, the pieces of evidence collected by a ..."
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Singular sources mining is essential in many applications like sensor fusion or dataset analysis. A singular source of information provides pieces of evidence that are significantly different from the majority of the other sources. In the DempsterShafer theory, the pieces of evidence collected
Singular sources in the Demiański–Newman spacetimes
, 2006
"... The analysis of singular regions in the NUT solutions carried out in the recent paper (Manko and Ruiz, 2005 Class. Quantum Grav. 22, 3555) is now extended to the Demiański–Newman vacuum and electrovacuum spacetimes. We show that the effect which produces the NUT parameter in a more general situation ..."
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The analysis of singular regions in the NUT solutions carried out in the recent paper (Manko and Ruiz, 2005 Class. Quantum Grav. 22, 3555) is now extended to the Demiański–Newman vacuum and electrovacuum spacetimes. We show that the effect which produces the NUT parameter in a more general
Singular Sources of Energy in Stars and Planets
, 706
"... If primordial lowmass black holes (PBH) exist in the Universe than many of stars and planetary bodies appear to be ”infected ” by them. This is also true in regard to the Sun and likely Jupiter and Saturn. The availability of even the very lowmass inner relativistic reactor may lead to essential c ..."
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If primordial lowmass black holes (PBH) exist in the Universe than many of stars and planetary bodies appear to be ”infected ” by them. This is also true in regard to the Sun and likely Jupiter and Saturn. The availability of even the very lowmass inner relativistic reactor may lead to essential changes in evolution scenario of a celestial body on its lifetime scale. Black holes in stellar interior may be found either in consequence of captures process or incorporation during the formation of a star from interstellar clouds. Surprisingly that in the equilibrium state a PBH growth is a longlived process with efolding rise time of billion years. One can envision a PBH orbiting inside the Sun. Our considerations showed that the PBH experiences very little friction in passing through the stellar matter. If the BH mass is above 10 −5 M ⊙ the major contribution to the luminosity comes from the relativistic gravitational reactor. In such a case a star evolves towards the Eddington limit. This should lead to considerable expansion of a star and a global stability loss. Microscopic PBHs can exist in the interior of planetary bodies too. To produce the required excess of thermal energy on Jupiter and Saturn the masses of
Numerical Approximations of Singular Source Terms in Differential Equations
 J. Comput. Phys
, 2003
"... Singular terms in di#erential equations pose severe challenges for numerical approximations on regular grids. Regularization of the singularities is a very useful technique for their representation on the grid. We analyze such techniques for the practically preferred case of narrow support of the ..."
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Cited by 51 (3 self)
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Singular terms in di#erential equations pose severe challenges for numerical approximations on regular grids. Regularization of the singularities is a very useful technique for their representation on the grid. We analyze such techniques for the practically preferred case of narrow support
Surface deformation due to shear and tensile faults in a halfspace
, 1985
"... A complete set of closed analytical expressions is presented in a unified manner for the internal displacements and strains due to shear and tensile faults in a halfspace for both point and finite rectangular sources. These expressions are particularly compact and systematically composed of terms r ..."
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Cited by 699 (1 self)
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A complete set of closed analytical expressions is presented in a unified manner for the internal displacements and strains due to shear and tensile faults in a halfspace for both point and finite rectangular sources. These expressions are particularly compact and systematically composed of terms
Collocation Methods for Hyperbolic Partial Differential Equations with Singular Sources
 Advances in Applied Mathematics and Mechanics
, 2009
"... Abstract. A numerical study is given on the spectral methods and the high order WENO finite difference scheme for the solution of linear and nonlinear hyperbolic partial differential equations with stationary and nonstationary singular sources. The singular source term is represented by the δfunct ..."
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Cited by 2 (1 self)
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Abstract. A numerical study is given on the spectral methods and the high order WENO finite difference scheme for the solution of linear and nonlinear hyperbolic partial differential equations with stationary and nonstationary singular sources. The singular source term is represented by the δ
Singular limits in a Liouvilletype equation with singular sources
 Houston J. Math
"... Abstract. This paper considers the existence of multiple blowing up solutions for a Liouvilletype equation −∆v = ε2ev − 4π ∑ αiδpi with homogeneous Dirichlet conditions, where δ is the Dirac mass. We construct a solution which blows up at singular sources and other m points, and the solution satisf ..."
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Cited by 1 (0 self)
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Abstract. This paper considers the existence of multiple blowing up solutions for a Liouvilletype equation −∆v = ε2ev − 4π ∑ αiδpi with homogeneous Dirichlet conditions, where δ is the Dirac mass. We construct a solution which blows up at singular sources and other m points, and the solution
A note on an extended clarifierthickener model with singular source and sink terms
 SCIENTIA SERIES A: MATHEMATICAL SCIENCES, VOL. 13 (2006), 36–44
, 2006
"... A onedimensional clarifierthickener (CT) model, which includes a singular feed source, can be expressed as a conservation law with a flux that is discontinuous with respect to the spatial variable. The CT model is extended herein by a singular sink through which material is extracted. The sink gi ..."
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Cited by 1 (0 self)
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A onedimensional clarifierthickener (CT) model, which includes a singular feed source, can be expressed as a conservation law with a flux that is discontinuous with respect to the spatial variable. The CT model is extended herein by a singular sink through which material is extracted. The sink
Results 1  10
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230,139