69
Views
1
CrossRef citations to date
0
Altmetric
Articles

Variational analysis for the heat kernels of Chandrasekhar-type operators

ORCID Icon
Pages 2457-2473 | Received 06 May 2017, Accepted 18 May 2017, Published online: 29 May 2017

References

  • Chandrasekhar S. Stochastic problems in physics and astronomy. Rev Modern Phys. 1943;15:1–89.
  • Case KM, Zweifel PF. Linear transport theory. Reading (MA): Addison-Wesley; 1967.
  • Tilinin IS, Jablonski A, Tougaard S. Path-length distribution of photoelectrons emitted from homogeneous noncrystalline solids: consequences for inelastic background analysis. Phys Rev B. 1995;52:5935–5945.
  • Jablonski A, Tilinin IS, Powell CJ. Mean escape depth of signal photoelectrons from amorphous and polycrystalline solids. Phys Rev B. 1996;54:10927–10937.
  • Jablonski A. The Chandrasekhar function revisited. Comp Phys Comm. 2015;196:416–428.
  • Das RN. Application of Wiener-Hopf technique to linear nonhomogeneous integral equations for a new representation of Chandrasekhar’s H-function in radiative transfer, its existence and uniqueness. J Math Anal Appl. 2008;337:1366–1382.
  • Das RN. Solution of Riemann-Hilbert problems for determination of new decoupled expressions of Chandrasekhar’s X- and Y-functions for slab geometry in radiative transfer. Astrophys Space Sci. 2010;326:91–103.
  • Smedley-Stevenson RP. A new analytic solution of the one-speed neutron transport equation for adjacent half-spaces with isotropic scattering. Ann Nucl Energ. 2012;46:218–231.
  • Hashem HHG, El-Sayed AMA. Stabilization of coupled systems of quadratic integral equations of Chandrasekhar type. Math Nachr. 2017;290:341–348.
  • Hachisu I, Kato M, Saio H, Nomoto K. A Single degenerate progenitor model for type Ia supernovae highly exceeding the Chandrasekhar mass limit. Astrophys J. 2012;744(69):15 p.
  • Kundu A, Mukhopadhyay B. Mass of highly magnetized white dwarfs exceeding the Chandrasekhar limit: an analytical view. Mod Phys Lett A. 2012;27(15):1250084.
  • Das U, Mukhopadhyay B. New mass limit for white dwarfs: super-Chandrasekhar type Ia supernova as a new standard candle. Phys Rev Lett. 2013;110(7):071102.
  • Chang D-C, Feng S-Y. Geometric analysis on Ornstein-Uhlenbeck operators with quadratic potentials. J Geom Anal. 2014;24:1211–1232.
  • Beals R, Gaveau B, Greiner PC. Complex Hamiltonian mechanics and parametrices for subelliptic Laplacians, I, II, III. Bull Sci Math. 1997;121:1–36. 97–149, 195–259
  • Calin O, Chang DC, Furutani K, et al. Heat Kernels for elliptic and sub-elliptic operators: methods and techniques. Boston: Birkhäuser; 2010.
  • Calin O, Chang DC, Tie J. Fundamental solutions for Hermite and subelliptic operators. J d’Analyse Math. 2007;100:223–248.
  • Chang D-C, Feng S-Y. Geometric analysis on generalised Hermite operators. Adv Appl Math. 2011;47:710–771.
  • Feng S-Y. Fundamental solutions on partial differential operators of second order with application to matrix Riccati equations. Taiwanese J Math. 2013;17:379–406.
  • Beals R. A note on fundamental solutions. Comm PDE. 1999;24:369–376.
  • Aarão J. A transport equation of mixed type. J Differ Equ. 1998;150:188–202.
  • Aarão J. Fundamental solutions for some partial differential operators from fluid dynamics and statistical physics. SIAM Rev. 2007;49:303–314.
  • Cercignani C. The Boltzmann equation and its applications. New York (NY): Springer-Verlag; 1988.
  • Lions P-L. On Boltzmann and Landau equations. Philos Trans Roy Soc London Ser A. 1994;346:191–204.
  • Chapman S, Cowling TG. The mathematical theory of nonuniform gases. 3rd ed. Cambridge: Cambridge University Press; 1990.
  • Duderstadt JJ, Martin WR. Transport theory. New York (NY): Wiley; 1979.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.