International Scientific Journal

Authors of this Paper

External Links


A family of variational principles is obtained for the 1-D inviscid flow by Ji-Huan He's semi-inverse method. The invalidy of the Lagrange multiplier method, e. g., the Lagrange crisis, is also discussed to eliminate constraints of a constrained variational principle. Two approaches to the elimination of the crisis are elucidated.
PAPER REVISED: 2021-10-01
PAPER ACCEPTED: 2021-10-01
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Issue 3, PAGES [2465 - 2469]
  1. He, J. H., A Fractal Variational Theory for One-Dimensional Compressible Flow in a Microgravity Space, Fractals, 28 (2020), 2, 2050024
  2. Wang, K. L., Yao, S. W., Fractal Variational Theory for Chaplygin-He Gas in a Microgravity Condition, J. Appl. Comput. Mech., 7 (2021), 1, pp. 182-188
  3. Chaplygin, S., On Gas Jets, Sci. Mem. Moscow Univ. Math. Phys., 1904, Vol. 21, pp. 1-121
  4. Lukovskii, I. A., Timokha, A. N., Bateman Variational Principle for a Class of Problems of Dynamics and Stability of Surface Waves, Ukrainian Mathematical Journal, 43 (1991), 3, pp. 1106-1110
  5. He, J. H., Hybrid Problems of Determining Unknown Shape of Bladings in Compressible S2-Flow in Mixed-Flow Turbomachinery via Variational Technique, Aircraft Engineering and Aerospace Technol-ogy, 71 (1999), 2, pp. 154-159
  6. He, J. H., Inverse Problems Of Determining The Unknown Shape Of Oscillating Airfoils In Compressi-ble 2D Unsteady Flow Via Variational Technique, Aircraft Engineering and Aerospace Technology, 72 (2000), 1, pp. 18-24
  7. Wang, K. L., He, C. H., A Remark on Wang's Fractal Variational Principle, Fractals, 27 (2019), 8, 1950134
  8. Wang, K. L., et al., Physical Insight of Local Fractional Calculus and its Application to Fractional KdV Burgers Kuramoto Equation, Fractals, 27 (2019), 7, 1950122
  9. He, J. H., Hamilton's Principle for Dynamical Elasticity, Appl. Math. Lett., 72 (2017), Oct., pp. 65-69
  10. Li, Y., He, C. H. A Short Remark on Kalaawy's Variational Principle for Plasma, Int. J. Numer. Method H., 27 (2017), 10, pp. 2203-2206
  11. He, J. H., Variational Principles for Some Non-linear Partial Differential Equations with Variable Coef-ficients, Chaos Soliton. Fract., 19 (2004), 4, pp. 847-851
  12. He, J. H., et al., A Fractal Modification of Chen-Lee-Liu Equation and its Fractal Variational Principle, International Journal of Modern Physics B, 35 (2021), 21, 2150214
  13. Wang, K. J., Generalized Variational Principle and Periodic Wave Solution to the Modified Equal width-Burgers Equation in Non-linear Dispersion Media, Physics Letters A, 419 (2021), Dec., 127723
  14. He, J. H., et al., Variational Approach to Fractal Solitary Waves, Fractals, 29 (2021), 7, 2150199
  15. Liu, X. Y., et al., Optimization of a Fractal Electrode-Level Charge Transport Model, Thermal Science, 25 (2021), 3, pp. 2213-2220
  16. Liu, Y. P., et al., A Fractal Langmuir Kinetic Equation and its Solution Structure, Thermal Science , 25 (2021), 2, pp. 1351-1354
  17. Liu, X. Y., et al., Computer Simulation of Pantograph Delay Differential Equation, Thermal Science, 25 (2021), 2, pp. 1381-1385
  18. He, J. H., et al., On a Strong Minimum Condition of a Fractal Variational Principle, Applied Mathemat-ics Letters, 119 (2021), Sept., 107199
  19. Tian, Y., Liu, J., Direct Algebraic Method for Solving Fractional Fokas Equation, Thermal Science, 25 (2021), 3, pp. 2235-2244
  20. Wang, K. J., et al., Investigation of the Periodic Solution of the Time-Space Fractional Sasa-Satsuma Equation Arising in the Monomode Optical Fibers, Vol. 137, No. 6, March 2022, 10.1209/0295-5075/ac2a62.
  21. Han, C., et al., Numerical Solutions of Space Fractional Variable-Coefficient KdV-Modified KdV Equa-tion by Fourier Spectral Method, Fractals, 29 (2021), 8, 21502467

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence