Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
W. Allard, The first variation of a varifold, Ann. of Math. 95 (1972), 417–491.
R. Courant, K.O. Friedrichs and H. Lewy, Über di Partilellen Differenzengleichungen der Mathematischen Physik, Math. Ann. 100 (1928), 32–74.
C.M. Dafermos and L. Hsiao, Hyperbolic systems of balance laws with inhomogeneity and dissipation, Indiana Univ. Mathematics J. 31 (1982), 471–491.
R.J. Di Perna, Global solutions to a class of nonlinear hyperbolic systems of equations, Comm. Pure and Appl. Math. 26 (1973), 1–28.
D. Fujiwara and S. Takakuwa, A varifold solution to the nonlinear equation of motion of a vibrating membrane, preprint Dept. of Mathematics, Tokyo Institute of Technology.
J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure and Appl. Math. 18 (1965), 697–715.
E. Giusti, Minimal surfaces and functions of bounded variation, Notes on Pure Mathematics 10 (1977), Australian National University, Canberra.
L. Hsiao and P. Marcati, A nonhomogeneous quasilinear hyperbolic system arising in chemical engineering, submitted.
P.D. Lax, Hyperbolic systems of conservation law, Comm. Pure and Appl. Math. 10 (1957), 537–566.
T.-P. Liu, Quasilinear hyperbolic systems, Comm. Math. Phys. 68 (1979), 141–172.
T.P. Liu, Hyperbolic conservation laws with relaxation and damping, Proceedings Int. Conf. L’Aquila 1986.
T.-P. Liu, The free piston problem for gas dynamics, J. Diff. Eqns 30 (1978), 175–191.
M. Miranda, Distribuzioni aventi derivate misure ed insiemi di perimetro localmente finito, Ann. Scuola Norm. Sup. Pisa 18 (1964), 27–56.
M. Miranda, Comportamento delle successioni convergenti di frontiere minimali, Rend. Sem. Mat. Univ. Padova 38 (1967), 238–257.
T. Nishida and J.A. Smoller, Mixed problems for nonlinear conservation laws, J. Diff. Eqns 23 (1977), 244–269.
J.A. Smoller, Schock waves and reaction-diffusion equations, Grundlehren der mathematischen Wissenschaften 258, Springer-Verlag, New York-Heidelberg-Berlin 1983.
Author information
Authors and Affiliations
Editor information
Additional information
Dedicated to Hans Lewy
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Marcati, P. (1988). Nonhomogeneous quasilinear hyperbolic systems: Initial and boundary value problem. In: Hildebrandt, S., Kinderlehrer, D., Miranda, M. (eds) Calculus of Variations and Partial Differential Equations. Lecture Notes in Mathematics, vol 1340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082896
Download citation
DOI: https://doi.org/10.1007/BFb0082896
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50119-0
Online ISBN: 978-3-540-45932-3
eBook Packages: Springer Book Archive