A variational formulation for constrained quasilinear vector systems
Author:
Nima Geffen
Journal:
Quart. Appl. Math. 35 (1977), 375-381
MSC:
Primary 76.49
DOI:
https://doi.org/10.1090/qam/459268
MathSciNet review:
459268
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Abstract: A variational formulation for multi-dimensional initial- and/or boundary-value problems for a system of quasilinear conservation equations with a rotationality condition in a vector form with the aid of a vector Lagrange multiplier is given. The duality between the physical and ’phase’ (or hodograph) spaces emerges, and the Lagrange multiplier turns out to be the vector potential for the conserved field, and hence of some interest in itself. Application is given to a family of transonic flows in the physical and hodograph planes, and to a problem in nonlinear sound propagation.
M. E. Gurtin, Variational principles for linear initial-value problems, Quart. Appl. Math. 22, 252–256 (1964)
B. Noble, Variational finite element methods for initial value problems, in The mathematics of finite elements applications, J. R. Whiteman, ed., Academic Press, 1973
- Enzo Tonti, On the variational formulation for linear initial value problems, Ann. Mat. Pura Appl. (4) 95 (1973), 331–359 (English, with Italian summary). MR 328715, DOI https://doi.org/10.1007/BF02410725
I. Herrera and J. Bielak, A simplified version of Gurtin’s variational principles, J. Rat. Mech. 53, 131–149 (1974)
- J. N. Reddy, A note on mixed variational principles for initial-value problems, Quart. J. Mech. Appl. Math. 28 (1975), 123–132. MR 361438, DOI https://doi.org/10.1093/qjmam/28.1.123
N. Geffen and S. Yaniv, A note on the variational formulation for quasilinear initial value problems, ZAMP.
- Ismael Herrera and Jacobo Bielak, Dual variational principles for diffusion equations, Quart. Appl. Math. 34 (1976), no. 1, 85–102. MR 467481, DOI https://doi.org/10.1090/S0033-569X-1976-0467481-1
- N. J. Yu and R. Seebass, Computational procedures for mixed equations with shock waves, Computational methods in nonlinear mechanics (Proc. Internat. Conf., Austin, Tex., 1974) Texas Inst. Comput. Mech., Austin, Tex., 1974, pp. 499–508. MR 0424009
H. Lomax, R. Bailey, and W. F. Ballhaus, On the numerical simulation of three-dimensional transonic flow with application to the C-141 wing, NASA TN D-6933, August 1973
M. E. Gurtin, Variational principles for linear initial-value problems, Quart. Appl. Math. 22, 252–256 (1964)
B. Noble, Variational finite element methods for initial value problems, in The mathematics of finite elements applications, J. R. Whiteman, ed., Academic Press, 1973
E. Tonti, On the variational formulation for linear initial-value problems, Ann. Math. Pura Appl. 95, 331–360 (1973)
I. Herrera and J. Bielak, A simplified version of Gurtin’s variational principles, J. Rat. Mech. 53, 131–149 (1974)
J. N. Reddy, A note on mixed variational principles for initial value problems, Quart. J. Mech. Appl. Math. 28, 123–132 (1975)
N. Geffen and S. Yaniv, A note on the variational formulation for quasilinear initial value problems, ZAMP.
I. Herrera and J. Bielak, Dual variational principles for diffusion equations, Quart. Appl. Math 34, 85–102 (1976)
N. J. Yu and R. Seebass, Computational procedures for mixed equations with shock waves, in Computational methods in nonlinear mechanics, T. J. Oden. ed., 1974, pp. 499–508.
H. Lomax, R. Bailey, and W. F. Ballhaus, On the numerical simulation of three-dimensional transonic flow with application to the C-141 wing, NASA TN D-6933, August 1973
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© Copyright 1977
American Mathematical Society