A one-dimensional inviscid and compressible fluid in a harmonic potential well

Acta Applicandae Mathematicae

Volumn 99, Issue 2, 2007, Pages 161-183

  Choquard, Philippe ^a   Strömberg, Thomas ^b  

^a EPFL   (Switzerland)

^b LULEÅ UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Continuity equation; Correlated initial conditions; Hamilton Jacobi equation; Measure solution; Viscosity solution

Indexed keywords

CORRELATION METHODS; DATA REDUCTION; HAMILTONIANS; NUMERICAL METHODS;

CONTINUITY EQUATION; CORRELATED INITIAL CONDITIONS; HAMILTON-JACOBI EQUATION; MEASURE SOLUTION; VISCOSITY SOLUTION;

HARMONIC ANALYSIS;

EID: 35548982191     PISSN: 01678019     EISSN: 15729036     Source Type: Journal    
DOI: 10.1007/s10440-007-9161-7     Document Type: Article

References (18)

1. Ben-Moussa, B., Kossioris, G.T.: On the system of Hamilton-Jacobi and transport equations arising in geometrical optics. Commun. Partial Differ. Equ. 28, 1085-1111 (2003)
2. Bouchut, F., James, F.: One-dimensional transport equations with discontinuous coefficients. Nonlinear Anal. 32, 891-933 (1998)
3. Brenier, Y., Grenier, E.: Sticky particles and scalar conservation laws. SIAM J. Numer. Anal. 35, 2317-2328 (1998)
4. Cannarsa, P., Sinestrari, C.: Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control. Progress in Nonlinear Differential Equations and Their Applications, vol. 58. Birkhäuser, Boston (2004)
5. Choquard, P.: Toward a canonical-Hamiltonian and microscopic field theory of classical liquids. Phys. A 279, 49-59 (2000)
6. Choquard, P., Wagner, J.: On the "mean-field" interpretation of Burgers' equation. J. Stat. Phys. 116, 843-853 (2004)
7. Conway, E.: Generalized solutions of linear differential equations with discontinuous coefficients and the uniqueness question for multidimensional quasilinear conservation laws. J. Math. Anal. Appl. 18, 238-251 (1967)
8. Crandall, M.G., Ishii, H., Lions, P.-L.: User's guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. (N.S.) 27, 1-67 (1992)
9. Filippov, A.F.: Differential equations with discontinuous right-hand side. Mat. Sb. (N.S.) 51(93), 99-128 (1960); Am. Math. Soc. Transl. (2) 42, 199-231 (1964)
10. Frisch, U., Bec, J., Villone, B.: Singularities and the distribution of density in the Burgers/adhesion model. Advances in nonlinear mathematics and science. Phys. D 152/153, 620-635 (2001)
11. Gosse, L., James, F.: Convergence results for an inhomogeneous system arising in various high frequency approximations. Numer. Math. 90, 721-753 (2002)
12. Hörmander, L.: Lectures on Nonlinear Hyperbolic Differential Equations. Mathématiques & Applications, vol. 26. Springer, Berlin (1997)
13. Lions, P.-L.: Generalized Solutions of Hamilton-Jacobi Equations. Research Notes in Mathematics, vol. 69. Pitman, Boston/London (1982) (Advanced Publishing Program)
14. Poupaud, F., Rascle, M.: Measure solutions to the linear multi-dimensional transport equations with non-smooth coefficients. Commun. Partial Differ. Equ. 22, 337-358 (1997)
15. Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren der Mathematischen Wissenschaften, vol. 317. Springer, Berlin (1998)
16. Strömberg, T.: On viscosity solutions of the Hamilton-Jacobi equation. Hokkaido Math. J. 28, 475-506 (1999)
17. Strömberg, T.: The Hopf-Lax formula gives the unique viscosity solution. Differ. Integral Equ. 15, 47-52 (2002)
18. Strömberg, T.: Hamilton-Jacobi equations having only action functions as solutions. Arch. Math. (Basel) 83, 437-449 (2004)