Convergence of approximate solutions to scalar conservation laws by degenerate diffusion

Pierangelo Marcati

Rendiconti del Seminario Matematico della Università di Padova (1989)

  • Volume: 81, page 65-78
  • ISSN: 0041-8994

How to cite

top

Marcati, Pierangelo. "Convergence of approximate solutions to scalar conservation laws by degenerate diffusion." Rendiconti del Seminario Matematico della Università di Padova 81 (1989): 65-78. <http://eudml.org/doc/108147>.

@article{Marcati1989,
author = {Marcati, Pierangelo},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {existence of weak solutions; scalar conservation laws; compensated compactness},
language = {eng},
pages = {65-78},
publisher = {Seminario Matematico of the University of Padua},
title = {Convergence of approximate solutions to scalar conservation laws by degenerate diffusion},
url = {http://eudml.org/doc/108147},
volume = {81},
year = {1989},
}

TY - JOUR
AU - Marcati, Pierangelo
TI - Convergence of approximate solutions to scalar conservation laws by degenerate diffusion
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1989
PB - Seminario Matematico of the University of Padua
VL - 81
SP - 65
EP - 78
LA - eng
KW - existence of weak solutions; scalar conservation laws; compensated compactness
UR - http://eudml.org/doc/108147
ER -

References

top
  1. [1] B. Dacorogna, Weak Continuity and Weak Lower Semicontinuity of Non-Linear Functionals, Lecture Notes in Mathematics, 922, Springer-Verlag, Berlin-Heidelberg-New York (1982). Zbl0484.46041MR658130
  2. [2] R.J. Di Perna, Convergence of approximate solutions to conservation laws, Arch. Rat. Mech. Anal., 82 (1983), pp. 27-70. Zbl0519.35054MR684413
  3. [3] P.D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, SIAM Reg. Conference Series in Applied Mathematics, Philadelphia (1973). Zbl0268.35062MR350216
  4. [4] P.L. Lions, Generalized Solutions of Hamilton-Jacobi Equations, Research Notes in Mathematics, 69, Pitman, London (1982). Zbl0497.35001MR667669
  5. [5] F. Murat, Compacité par compensation, Ann. Sc. Norm. Pisa, Sci. Fis. Mat., 5 (1978), pp. 489-507. Zbl0399.46022MR506997
  6. [6] O.A. Oleinik, Discontinuous solutions of nonlinear differential equations, Uspekhi Mat. Nauk (N.S.), 12, n. 3(75) (1957), pp. 3-73 (English transl. in Amer. Math. Soc. Transl. Ser. 2, vol. 26, pp. 95-172). Zbl0131.31803MR94541
  7. [7] S. Osher - J. Ralston, L1 stability of travelling waves with applications to convective porous media flow, Comm. Pure Appl. Math., 35 (1982), pp. 737-749. Zbl0479.35053MR673828
  8. [8] L. Tartar, Compensated compactness and applications to partial differential equations, in Research Notes in Mathematics, Nonlinear Analysis and Mechanics: Herriot- Watt Symposium, Vol. 4, ed. R. J. KNOPS, Pitman (1979). Zbl0437.35004MR584398
  9. [9] L. Tartar, The compensated compactness method applied to systems of conservation laws, in Nonlinear PDEs, J. BALL (Ed.), D. Reidel Publishing Company (1983). Zbl0536.35003MR725524
  10. [10] L. Van Hove, Sur l'extension de la condition de Legendre du calcul des variations aux integrales multiples à plusieurs fonction inconnues, Nederl. Akad. Weten., 50 (1947), pp. 18-23. Zbl0029.26802MR20223
  11. [11] A.I. Vol'pert - S.I. Hudjaev, Cauchy problem for degenerate second order quasilinear parabolic equations, Math. USSR Sbornik, 7 (1969), pp. 365-387. Zbl0191.11603
  12. [12] J.I. Diaz - R. Kersner, Nonexistence d'une des frontières libres dans une équation dégenerée en theorie de la filtration, C. R. Acad. Sc. Paris, 296, Série I (28 mars 1983), pp. 505-508. Zbl0543.35102MR702558
  13. [13] J.I. Diaz - R. Kersner, On a nonlinear degenerate parabolic equation in infiltration or evaporation through a porous medium, MRC Tech. Summ. Rep. (University of Wisconsin) (1983). Zbl0634.35042
  14. [14] B.H. Gilding, A nonlinear degenerate parabolic equation, Ann. Sc. Norm. Pisa, Sci. Fis. Mat., 4 (1977), pp. 393-432. Zbl0364.35027MR509720
  15. [15] B.H. Gilding - L.A. Peletier, The Cauchy problem for an equation in the theory of infiltration, Arch. Rat. Mech. Anal., 61 (1976), pp. 127-140. Zbl0336.76037MR408428
  16. [16] E. Di Benedetto, Continuity of weak solutions to a general porous medium equation, Indiana Univ. Math. J., 32 (1983), pp. 83-118. Zbl0526.35042MR684758
  17. [17] O.A. Oleinik, Uniqueness and stability of the generalized solution of the Cauchy problem for a quasilinear equation, Usp. Mat. Nauk., 14 (1959), pp. 165-170 (English transl. in Amer. Math. Soc. Transl. Ser. 2, 23 (1964), pp. 285-290). Zbl0132.33303MR117408
  18. [18] M. Crandall, The semigroup approach to first order quasilinear equation in several space variables, Israel J. Math., 12 (1972), pp. 108-132. Zbl0246.35018MR316925
  19. [19] P. Marcati, Approximate solutions to conservation laws via convective parabolic equations, to appearComm. P.D.E. (1988). Zbl0653.35057MR917603

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.