On a nonhomogeneous system of pressureless flow

Authors:
Yi Ding and Feimin Huang

Journal:
Quart. Appl. Math. **62** (2004), 509-528

MSC:
Primary 35L60; Secondary 35D05, 35L65, 76N10

DOI:
https://doi.org/10.1090/qam/2086043

MathSciNet review:
MR2086043

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, a nonhomogeneous system of pressureless flow

**[1]**F.Bouchut, On zero pressure gas dynamics,*Advances in kinetic theory and computing, Series on Advances in Mathematics for Applied Sciences*, World Scientific, Vol.22: 171-190 (1994). MR**1323183****[2]**F. Bouchut and F. James, One-dimensional transportation equations with discontinuous coefficients,*Nonlinear Analysis TMA*, 32 (1998), 891-933. MR**1618393****[3]**F. Bouchut and F. James, Duality solutions for pressureless gases, monotone scalar conservation laws, and uniqueness,*Comm. Part. Diff. Equs*., 24 (1999), 2173-2190. MR**1720754****[4]**Y. Brenier and E. Grenier, Sticky particles and scalar conservation laws,*SIAM J. Num. Analysis*, Vol. 35, No. 6, 1998, 2317-2328. MR**1655848****[5]**C. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws,*Indiana Univ. Math. Journal*, Vol. 26, No. 6 (1977): 1097-1119. MR**0457947****[6]**G. Dal Maso, P. Le Floch, and F. Murat, Definition and weak stability of nonconservative products,*J. Math. Pure Appl*. 74 (1995), 483-548. MR**1365258****[7]**X. Ding, Q. Jiu, and C. He, On a nonhomogeneous Burger's equation, Sci. China Ser. A, 44 (2001), No. 8 984-993. MR**1857553****[8]**X. Ding and Y. Ding, Viscosity method of a non-homogeneous Burgers equation, 2002, preprint.**[9]**W. E, Y. Rykov, and Y. Sinai, Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics,*Comm. Math. Phys*., 177 (1996), 349-380. MR**1384139****[10]**E. Hopf, The partial differential equation ,*Comm. Pure Appl. Math*., 1950, 3: 201-230.**[11]**F. Huang and Z. Wang, Well posedness for pressureless flow,*Comm. Math. Phys*. 222 (2001), no. 1, 117-146. MR**1853866****[12]**S. Chen, J. Li, and T. Zhang, Explicit construction of measure solutions of the Cauchy problem for the transportation equations,*Science in China (Series A)*, Vol. 40, 12: 1287-1299(1997). MR**1613902****[13]**O. Oleinik, Discontinuous solutions of nonlinear differential equations,*Amer. Math. Soc. Transl*. (2), 26 (1963), 95-172. MR**0151737****[14]**F. Poupaud and M. Rascle, Measure solutions to the linear multidimensional transportation with discontinuous coefficients,*Comm. Part. Diff. Equs*., 22 (1997), 337-358. MR**1434148****[15]**Z. Wang, F. Huang, and X. Ding, On the Cauchy problem of transportation equation,*Acta Math. Appl. Sinica*, No. 2, 1997, 113-122. MR**1443942****[16]**Z. Wang and X. Ding, Uniqueness of generalized solution for the Cauchy problem of transportation equations,*Acta Math. Scientia*17 (1997), n. 3, 341-352. MR**1483969**

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
35L60,
35D05,
35L65,
76N10

Retrieve articles in all journals with MSC: 35L60, 35D05, 35L65, 76N10

Additional Information

DOI:
https://doi.org/10.1090/qam/2086043

Article copyright:
© Copyright 2004
American Mathematical Society