Dual variational principles for diffusion equations

Herrera, Ismael; Bielak, Jacobo

doi:10.1090/qam/467481

Authors: Ismael Herrera and Jacobo Bielak
Journal: Quart. Appl. Math. 34 (1976), 85-102
MSC: Primary 49G99
DOI: https://doi.org/10.1090/qam/467481
MathSciNet review: 467481
Full-text PDF

[1] I. Javandel and P. A. Witherspoon, A method of analyzing transient fluid flow in multilayered aquifers, Water Resour. Res. 5, 856-869 (1969)
[2] S. P. Neuman and P. A. Witherspoon, Transient flow of ground water to wells in multiple aquifer systems, Geotechnical Engineering Report 69-1, University of California, Berkeley (1969)
[3] B. Noble and M. J. Sewell, On dual extremum principles in applied mathematics, J. Inst. Math. Appl. 9 (1972), 123–193. MR 0307012
[4] B. Noble, Complementary variational principles for boundary value problems, I. Basic principles, Report No. 473, Math. Research Center, University of Wisconsin (1964)
[5] M. J. Sewell, On dual approximation principles and optimization in continuum mechanics, Philos. Trans. Roy. Soc. London Ser. A 265 (1969/1970), 319–351. MR 0255124, https://doi.org/10.1098/rsta.1969.0059
[6] Arnold Magowan Arthurs, Complementary variational principles, 2nd ed., The Clarendon Press, Oxford University Press, New York, 1980. Oxford Mathematical Monographs. MR 594935
[7] Peter D. Robinson, Complementary variational principles, Nonlinear Functional Anal. and Appl. (Proc. Advanced Sem., Math. Res. Center, Univ. of Wisconsin, Madison, Wis., 1970) Academic Press, New York, 1971, pp. 507–576. MR 0283653
[8] M. J. Sewell, The governing equations and extremum principles of elasticity and plasticity generated from a single functional. Part I, J. Struct. Mech. 2, 1-32 (1973)
[9] M. J. Sewell, The governing equations and extremum principles of elasticity and plasticity generated from a single functional. Part II, J. Struct. Mech. 2, 135-158 (1973)
[10] I. Herrera, A general formulation of variational principles, Instituto de Ingeniería, UNAM, E 10, México, D.F. (1974)
[11] M. Z. Nashed, Differentiability and related properties of nonlinear operators: Some aspects of the role of differentials in nonlinear functional analysis, Nonlinear Functional Anal. and Appl. (Proc. Advanced Sem., Math. Res. Center, Univ. of Wisconsin, Madison, Wis., 1970) Academic Press, New York, 1971, pp. 103–309. MR 0276840
[12] M. M. Vainberg, Variational methods in the study of non-linear operator equations, Holden-Day, San Francisco, 1964
[13] I. Herrera and J. Bielak, A simplified version of Gurtin's variational principles, Arch. Rat. Mech. Anal. 53, 131-149 (1974)
[14] R. S. Sandhu and K. S. Pister, Variational methods in continuous mechanics, in International conference on variational methods in engineering, Southampton University, England, 1.13-1.25 (1972)
[15] E. Tonti, A systematic approach to the search for variational principle, in International conference on variational methods in engineering, Southampton University, England, 1.1-1.12 (1972)
[16] 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 0328715, https://doi.org/10.1007/BF02410725
[17] Vadim Komkov, Application of Rall’s theorem to classical elastodynamics, J. Math. Anal. Appl. 14 (1966), 511–521. MR 0205525, https://doi.org/10.1016/0022-247X(66)90011-4
[18] A. M. Arthurs, A note on Komkov’s class of boundary value problems and associated variational principles, J. Math. Anal. Appl. 33 (1971), 402–407. MR 0271515, https://doi.org/10.1016/0022-247X(71)90064-3
[19] S. P. Neuman and P. A. Witherspoon, Variational principles for confined and unconfined flow of ground water, Water Resour. Res. 5, 1376-1382 (1970)
[20] S. P. Neuman and P. A. Witherspoon, Variational principles for fluid flow in porous media, J. Eng. Mech. Div. ASCE 97, 359-374 (1971)
[21] M. E. Gurtin, Variational principles for linear initial value problems, Quart. Appl. Math. 22, 252-256 (1964)