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Journal articles on the topic 'Coupled evolution equations'

Author: Grafiati

Published: 14 September 2024

Last updated: 31 July 2025

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1

Maruszewski, Bogdan. "Coupled evolution equations of deformable semiconductors." International Journal of Engineering Science 25, no. 2 (1987): 145–53. http://dx.doi.org/10.1016/0020-7225(87)90002-4.

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2

Yusufoğlu, Elcin, and Ahmet Bekir. "Exact solutions of coupled nonlinear evolution equations." Chaos, Solitons & Fractals 37, no. 3 (2008): 842–48. http://dx.doi.org/10.1016/j.chaos.2006.09.074.

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3

Nakagiri, Shin-ichi, and Jun-hong Ha. "COUPLED SINE-GORDON EQUATIONS AS NONLINEAR SECOND ORDER EVOLUTION EQUATIONS." Taiwanese Journal of Mathematics 5, no. 2 (2001): 297–315. http://dx.doi.org/10.11650/twjm/1500407338.

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4

Zhao, Dan, and Zhaqilao. "Darboux transformation approach for two new coupled nonlinear evolution equations." Modern Physics Letters B 34, no. 01 (2019): 2050004. http://dx.doi.org/10.1142/s0217984920500049.

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A new coupled Burgers equation and a new coupled KdV equation which are associated with [Formula: see text] matrix spectial problem are investigated for complete integrability and covariant property. For integrability, Lax pair and conservation laws of the two new coupled equations with four potentials are established. For covariant property, Darboux transformation (DT) is used to construct explicit solutions of the two new coupled equations.

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5

Khan, K., and M. A. Akbar. "Solitary Wave Solutions of Some Coupled Nonlinear Evolution Equations." Journal of Scientific Research 6, no. 2 (2014): 273–84. http://dx.doi.org/10.3329/jsr.v6i2.16671.

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In this article, the modified simple equation (MSE) method has been executed to find the traveling wave solutions of the coupled (1+1)-dimensional Broer-Kaup (BK) equations and the dispersive long wave (DLW) equations. The efficiency of the method for finding exact solutions has been demonstrated. It has been shown that the method is direct, effective and can be used for many other nonlinear evolution equations (NLEEs) in mathematical physics. Moreover, this procedure reduces the large volume of calculations. Keywords: MSE method; NLEE; BK equations; DLW equations; Solitary wave solutions. © 2

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6

Malfliet, W. "Travelling-wave solutions of coupled nonlinear evolution equations." Mathematics and Computers in Simulation 62, no. 1-2 (2003): 101–8. http://dx.doi.org/10.1016/s0378-4754(02)00182-9.

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7

Alabau, F., P. Cannarsa, and V. Komornik. "Indirect internal stabilization of weakly coupled evolution equations." Journal of Evolution Equations 2, no. 2 (2002): 127–50. http://dx.doi.org/10.1007/s00028-002-8083-0.

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8

RYDER, E., and D. F. PARKER. "Coupled evolution equations for axially inhomogeneous optical fibres." IMA Journal of Applied Mathematics 49, no. 3 (1992): 293–309. http://dx.doi.org/10.1093/imamat/49.3.293.

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9

Khan, Kamruzzaman, and M. Ali Akbar. "Traveling Wave Solutions of Some Coupled Nonlinear Evolution Equations." ISRN Mathematical Physics 2013 (May 20, 2013): 1–8. http://dx.doi.org/10.1155/2013/685736.

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The modified simple equation (MSE) method is executed to find the traveling wave solutions for the coupled Konno-Oono equations and the variant Boussinesq equations. The efficiency of this method for finding exact solutions and traveling wave solutions has been demonstrated. It has been shown that the proposed method is direct, effective, and can be used for many other nonlinear evolution equations (NLEEs) in mathematical physics. Moreover, this procedure reduces the large volume of calculations.

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10

Hassaballa, Abaker A., Fathea M. O. Birkea, Ahmed M. A. Adam, et al. "Multiple and Singular Soliton Solutions for Space–Time Fractional Coupled Modified Korteweg–De Vries Equations." International Journal of Analysis and Applications 22 (April 22, 2024): 68. http://dx.doi.org/10.28924/2291-8639-22-2024-68.

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The focus of this paper is on the nonlinear coupled evolution equations, specifically within the context of the fractional coupled modified Korteweg–de Vries (mKdV) equation, employing the conformable fractional derivative (CFD) approach. The primary objective of this paper is to thoroughly investigate the applicability of the Hirota bilinear method for deriving analytical solutions to the fractional mKdV equations. A range of exact analytical solutions for the fractional coupled mKdV equations is obtained. The findings in general indicate that the Hirota bilinear method is an effective approa

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11

Wan, Qian, and Ti-Jun Xiao. "Exponential Stability of Two Coupled Second-Order Evolution Equations." Advances in Difference Equations 2011 (2011): 1–14. http://dx.doi.org/10.1155/2011/879649.

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12

Arafa, A. A. M., and S. Z. Rida. "Numerical solutions for some generalized coupled nonlinear evolution equations." Mathematical and Computer Modelling 56, no. 11-12 (2012): 268–77. http://dx.doi.org/10.1016/j.mcm.2011.12.046.

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13

Seadawy, A. R., and K. El-Rashidy. "Traveling wave solutions for some coupled nonlinear evolution equations." Mathematical and Computer Modelling 57, no. 5-6 (2013): 1371–79. http://dx.doi.org/10.1016/j.mcm.2012.11.026.

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14

Hao, Jianghao, Zhaobin Kuang, Zhuangyi Liu, and Jiongmin Yong. "Stability analysis for two coupled second order evolution equations." Journal of Differential Equations 432 (July 2025): 113246. https://doi.org/10.1016/j.jde.2025.113246.

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15

Liu, Wenyuan, Wei Xia, and Shengping Shen. "Fully Coupling Chemomechanical Yield Theory Based on Evolution Equations." International Journal of Applied Mechanics 08, no. 04 (2016): 1650058. http://dx.doi.org/10.1142/s1758825116500587.

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Coupling chemomechanical yield is one of the key issues in the oxidation of metal and polymer matrix materials. In this paper, the evolving equations for fully coupled thermal–chemical–mechanical processes were derived using the theory of thermodynamics. Then, the coupled chemomechanical yield condition and flow rule were directly obtained from the evolution equations by extending the von Mises theory of plasticity. The coupled yield condition reveals that only the chemical reactions or diffusions may lead to the yield of material even without the mechanical stress, which significantly differs

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16

Elwakil, Elsayed Abd Elaty, and Mohamed Aly Abdou. "New Applications of the Homotopy Analysis Method." Zeitschrift für Naturforschung A 63, no. 7-8 (2008): 385–92. http://dx.doi.org/10.1515/zna-2008-7-801.

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An analytical technique, namely the homotopy analysis method (HAM), is applied using a computerized symbolic computation to find the approximate and exact solutions of nonlinear evolution equations arising in mathematical physics. The HAM is a strong and easy to use analytic tool for nonlinear problems and does not need small parameters in the equations. The validity and reliability of the method is tested by application on three nonlinear problems, namely theWhitham-Broer-Kaup equations, coupled Korteweg-de Vries equation and coupled Burger’s equations. Comparisons are made between the result

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17

Han, Ding, Bing Gen Zhan, and Xiao Ming Huang. "Fatigue Analysis of the Asphalt Mixture Beam Using Damage Evolution Equations." Advanced Materials Research 163-167 (December 2010): 3332–35. http://dx.doi.org/10.4028/www.scientific.net/amr.163-167.3332.

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Damage evolution equations of asphalt mixture specimen beams were analyzed using the fracture toughness index and the ultimate tension strain index, respectively. The fracture toughness of the asphalt mixture was calculated by FEM. Damage evolution equations controlled apart by the stress and the strain were given. Their coefficients were back-calculated using partial fatigue tests data. The fully coupled stress-damage method and the fully coupled strain-damage method were used. The life prediction precision of each equation was verified by residual fatigue tests data. The results show that FE

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18

Junker, Philipp, and Daniel Balzani. "An extended Hamilton principle as unifying theory for coupled problems and dissipative microstructure evolution." Continuum Mechanics and Thermodynamics 33, no. 4 (2021): 1931–56. http://dx.doi.org/10.1007/s00161-021-01017-z.

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AbstractAn established strategy for material modeling is provided by energy-based principles such that evolution equations in terms of ordinary differential equations can be derived. However, there exist a variety of material models that also need to take into account non-local effects to capture microstructure evolution. In this case, the evolution of microstructure is described by a partial differential equation. In this contribution, we present how Hamilton’s principle provides a physically sound strategy for the derivation of transient field equations for all state variables. Therefore, we

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19

MA, WEN-XIU. "AKNS Type Reduced Integrable Hierarchies with Hamiltonian Formulations." Romanian Journal of Physics 68, no. 9-10 (2023): 116. http://dx.doi.org/10.59277/romjphys.2023.68.116.

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"The aim of this paper is to generate a kind of integrable hierarchies of four-component evolution equations with Hamiltonian structures, from a kind of reduced Ablowitz-Kaup-Newell-Segur (AKNS) matrix spectral problems. The zero curvature formulation is the basic tool and the trace identity is the key to establishing Hamiltonian structures. Two examples of Hamiltonian equations in the resulting inte- grable hierarchies are added to the category of coupled integrable nonlinear Schr¨odinger equations and coupled integable modified Korteweg-de Vries equations."

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20

Roy, P. K. "An integrable system governed by coupled non-linear evolution equations." Il Nuovo Cimento A 109, no. 11 (1996): 1613–15. http://dx.doi.org/10.1007/bf02778246.

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21

Abdelkawy, M. A., A. H. Bhrawy, E. Zerrad, and A. Biswas. "Application of Tanh Method to Complex Coupled Nonlinear Evolution Equations." Acta Physica Polonica A 129, no. 3 (2016): 278–83. http://dx.doi.org/10.12693/aphyspola.129.278.

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22

Kovriguine, Dmitrij, та Alexandr Potapov. "Nonlinear wave dynamics of one-dimensional elastic systems. Part I. Method оf coupled normal waves". Izvestiya VUZ. Applied Nonlinear Dynamics 4, № 2 (1996): 72–80. https://doi.org/10.18500/0869-6632-1996-4-2-72-80.

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In present paper the theoretical wave approach is developed for investigation of nonlinear dynamics of one-dimensional elastic systems with a strong dispersion. A technique is proposed to reduce the physical field equations to those for nonlinearity coupled normal waves. Then the equations of coupled normal waves are reduced to the evolution equations, which describe either multiwave resonant interaction or wave self-modulation or group synchronism between short and long waves, depending on a problem formulation.

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23

Alzaidy, J. F. "Extended Mapping Method and Its Applications to Nonlinear Evolution Equations." Journal of Applied Mathematics 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/597983.

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We use extended mapping method and auxiliary equation method for finding new periodic wave solutions of nonlinear evolution equations in mathematical physics, and we obtain some new periodic wave solution for the Boussinesq system and the coupled KdV equations. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics.

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24

Debsarma, S., S. Senapati, and K. P. Das. "Nonlinear Evolution Equations for Broader Bandwidth Wave Packets in Crossing Sea States." International Journal of Oceanography 2014 (June 9, 2014): 1–9. http://dx.doi.org/10.1155/2014/597895.

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Two coupled nonlinear equations are derived describing the evolution of two broader bandwidth surface gravity wave packets propagating in two different directions in deep water. The equations, being derived for broader bandwidth wave packets, are applicable to more realistic ocean wave spectra in crossing sea states. The two coupled evolution equations derived here have been used to investigate the instability of two uniform wave trains propagating in two different directions. We have shown in figures the behaviour of the growth rate of instability of these uniform wave trains for unidirection

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25

Schneider, Guido. "Justification of mean-field coupled modulation equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 127, no. 3 (1997): 639–50. http://dx.doi.org/10.1017/s0308210500029942.

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We are interested in reflection symmetric (x↦–x) evolution problems on the infinite line. In the systems which we have in mind, a trivial ground state loses stability and bifurcates into a temporally oscillating, spatial periodic pattern. A famous example of such a system is the Taylor-Couette problem in the case of strongly counter-rotating cylinders. In this paper, we consider a system of coupled Kuramoto–Shivashinsky equations as a model problem for such a system. We are interested in solutions which are slow modulations in time and in space of the bifurcating pattern. Multiple scaling anal

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26

Hua, Yuan, Bao Hua Lv, and Tai Quan Zhou. "Parametric Variational Principle for Solving Coupled Damage Problem." Key Engineering Materials 348-349 (September 2007): 813–16. http://dx.doi.org/10.4028/www.scientific.net/kem.348-349.813.

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The parametric variational principle adopts the extreme variational idea in the modern control theory and uses state equations deduced from the constitutive law to control the functional variation, which is an effective solution to the nonlinear equations. Based on the fundamental equations of elasto-plasticity coupled damage problem, the potential functional of elasto-plasticity is constructed. Also the state equations with approximation of damage evolution equation and load functions are constructed in the paper. The solution of elasto-plasticity damage problem can be deduced to solve proble

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27

El-Aqqad, Brahim. "The equations coupled by Von Karman system with thermoelasticity." Gulf Journal of Mathematics 17, no. 2 (2024): 190–207. http://dx.doi.org/10.56947/gjom.v17i2.2171.

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The aim of this paper is to study the model of the von Karman evolution coupled to the thermoelastic equation, with rotational inertia and clamped boundary conditions. We establish the existence and uniqueness of a weak solution related to the dynamic model. Towards the conclusion, we employ the finite difference method to approximate the solution to our problem.

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28

Carrington, M. E., R. Kobes, G. Kunstatter, D. Pickering, and E. Vaz. "Equilibration in an interacting field theory." Canadian Journal of Physics 80, no. 9 (2002): 987–93. http://dx.doi.org/10.1139/p02-065.

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We use a combination of perturbation theory and numerical techniques to study the equilibration of two interacting fields that are initially at thermal equilibrium at different temperatures. Using standard rules of quantum field theory, we examine the master equations that describe the time evolution of the distribution functions for the two coupled systems. By making a few reasonable assumptions we reduce the resulting coupled integral/differential equations to a pair of differential equations that can be solved numerically relatively easily and which give physically sensible results. PACS No

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29

Xu, Siqi, Xianguo Geng, and Bo Xue. "An extension of the coupled derivative nonlinear Schrödinger hierarchy." Modern Physics Letters B 32, no. 02 (2018): 1850016. http://dx.doi.org/10.1142/s0217984918500161.

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In this paper, a 3 × 3 matrix spectral problem with six potentials is considered. With the help of the compatibility condition, a hierarchy of new nonlinear evolution equations which can be reduced to the coupled derivative nonlinear Schrödinger (CDNLS) equations is obtained. By use of the trace identity, it is proved that all the members in this new hierarchy have generalized bi-Hamiltonian structures. Moreover, infinitely many conservation laws of this hierarchy are constructed.

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30

KHANI, F., M. T. DARVISHI, A. FARMANY, and L. KAVITHA. "NEW EXACT SOLUTIONS OF COUPLED (2+1)-DIMENSIONAL NONLINEAR SYSTEMS OF SCHRÖDINGER EQUATIONS." ANZIAM Journal 52, no. 1 (2010): 110–21. http://dx.doi.org/10.1017/s1446181111000563.

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AbstractThe Exp-function method is applied to construct a new type of solution of the coupled (2+1)-dimensional nonlinear system of Schrödinger equations. It is shown that the method provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.

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31

Erjaee, G. H., and M. Alnasr. "Phase Synchronization in Coupled Sprott Chaotic Systems Presented by Fractional Differential Equations." Discrete Dynamics in Nature and Society 2009 (2009): 1–10. http://dx.doi.org/10.1155/2009/753746.

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Phase synchronization occurs whenever a linearized system describing the evolution of the difference between coupled chaotic systems has at least one eigenvalue with zero real part. We illustrate numerical phase synchronization results and stability analysis for some coupled Sprott chaotic systems presented by fractional differential equations.

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32

Guesmia, Aissa. "Asymptotic behavior for coupled abstract evolution equations with one infinite memory." Applicable Analysis 94, no. 1 (2014): 184–217. http://dx.doi.org/10.1080/00036811.2014.890708.

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33

Tsang, S. C., and K. W. Chow. "The evolution of periodic waves of the coupled nonlinear Schrödinger equations." Mathematics and Computers in Simulation 66, no. 6 (2004): 551–64. http://dx.doi.org/10.1016/j.matcom.2004.04.002.

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34

da Silva Alves, Margareth, and Octavio Paulo Vera Villagrán. "Smoothing properties for a coupled system of nonlinear evolution dispersive equations." Indagationes Mathematicae 20, no. 2 (2009): 285–327. http://dx.doi.org/10.1016/s0019-3577(09)80015-3.

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35

Xiao, Ti-Jun, and Jin Liang. "Coupled second order semilinear evolution equations indirectly damped via memory effects." Journal of Differential Equations 254, no. 5 (2013): 2128–57. http://dx.doi.org/10.1016/j.jde.2012.11.019.

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36

Ghose, Chandana, and A. Roy Chowdhury. "Periodic inverse problem for a new hierarchy of coupled evolution equations." International Journal of Theoretical Physics 30, no. 7 (1991): 1033–39. http://dx.doi.org/10.1007/bf00673994.

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37

Bekir, Ahmet. "Applications of the extended tanh method for coupled nonlinear evolution equations." Communications in Nonlinear Science and Numerical Simulation 13, no. 9 (2008): 1748–57. http://dx.doi.org/10.1016/j.cnsns.2007.05.001.

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38

Hereman, Willy. "Exact solitary wave solutions of coupled nonlinear evolution equations using MACSYMA." Computer Physics Communications 65, no. 1-3 (1991): 143–50. http://dx.doi.org/10.1016/0010-4655(91)90166-i.

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39

Yaşar, Emrullah, and Sait San. "A Procedure to Construct Conservation Laws of Nonlinear Evolution Equations." Zeitschrift für Naturforschung A 71, no. 5 (2016): 475–80. http://dx.doi.org/10.1515/zna-2016-0057.

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AbstractIn this article, we established abundant local conservation laws to some nonlinear evolution equations by a new combined approach, which is a union of multiplier and Ibragimov’s new conservation theorem method. One can conclude that the solutions of the adjoint equations corresponding to the new conservation theorem can be obtained via multiplier functions. Many new families of conservation laws of the Pochammer–Chree (PC) equation and the Kaup–Boussinesq type of coupled KdV system are successfully obtained. The combined method presents a wider applicability for handling the conservati

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40

Shah, Ijaz, Ghazala Anwar, H. A. Shah, T. Abdullah, and M. Anis Alam. "Chaotic Evolution of a Parametric Instability in a Piezoelectric Semiconductor Plasma." International Journal of Bifurcation and Chaos 07, no. 05 (1997): 1103–13. http://dx.doi.org/10.1142/s021812749700090x.

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We consider the chaotic evolution of three parametrically interacting waves in a piezoelectric semiconductor plasma. The evolution equation has been derived using the coupled mode theory. The waves are an extraordinary wave, ordinary wave and upper hybrid acoustic wave. The extraordinary wave is a growing wave and the other two are damped modes. The equations are transformed and put in a standard form and made dimensionless by suitable substitution of new variables. Finally a set of three equations is obtained. The real and imaginary parts of the equations are then separated. The three imagina

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41

Gao, Yi-Tian, and Bo Tian. "Notiz: A Symbolic Computation-Based Method and Two Nonlinear Evolution Equations for Water Waves." Zeitschrift für Naturforschung A 52, no. 3 (1997): 295–96. http://dx.doi.org/10.1515/zna-1997-0311.

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Abstract A symbolic-computation-based method, which has been newly proposed, is considered for a (2+1)-dimensional generalization of shallow water wave equations and a coupled set of the (2 +1)-dimensional integrable dispersive long wave equations. New sets of soliton-like solutions are constructed, along with solitary waves.

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42

Li, Bang Qing, and Yu Lan Ma. "Exact Solutions for Coupled mKdV Equations by a New Symbolic Computation Method." Applied Mechanics and Materials 20-23 (January 2010): 184–89. http://dx.doi.org/10.4028/www.scientific.net/amm.20-23.184.

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By introducing (G′/G)-expansion method and symbolic computation software MAPLE, two types of new exact solutions are constructed for coupled mKdV equations. The solutions included trigonometric function solutions and hyperbolic function solutions. The procedure is concise and straightforward, and the method is also helpful to find exact solutions for other nonlinear evolution equations.

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43

FASANO, ANTONIO, DIETMAR HÖMBERG, and LUCIA PANIZZI. "A MATHEMATICAL MODEL FOR CASE HARDENING OF STEEL." Mathematical Models and Methods in Applied Sciences 19, no. 11 (2009): 2101–26. http://dx.doi.org/10.1142/s0218202509004054.

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A mathematical model for the case hardening of steel is presented. Carbon is dissolved in the surface layer of a low-carbon steel part at a temperature sufficient to render the steel austenitic, followed by quenching to form a martensitic microstructure. The model consists of a nonlinear evolution equation for the temperature, coupled with a nonlinear evolution equation for the carbon concentration, both coupled with two ordinary differential equations to describe the evolution of phase fractions. We investigate questions of existence and uniqueness of a solution and finally present some numer

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44

Yan, Zhenya. "Abundant New Exact Solutions of the Coupled Potential KdV Equation and the Modified KdV-Type Equation." Zeitschrift für Naturforschung A 56, no. 12 (2001): 809–15. http://dx.doi.org/10.1515/zna-2001-1203.

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Abstract Exact solutions of nonlinear evolution equations (NLEEs)in soliton theory and their applications are studied. A powerful method is established to search for exact travelling wave solutions of NLEEs. We chose the coupled potential KdV equation and modified KdV-type equations presented by Foursov to illustrate the approach with the aid of Maple. As a result, eight families of exact solutions of the coupled potential KdV equation and nine families of exact solutions of the modified KdV-type equations are obtained, which contain new kink-like soliton solutions, kink shaped solitons, bell

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45

Sekhar, Ashok, Alex D. Bain, Jessica A. O. Rumfeldt, Elizabeth M. Meiering, and Lewis E. Kay. "Evolution of magnetization due to asymmetric dimerization: theoretical considerations and application to aberrant oligomers formed by apoSOD12SH." Physical Chemistry Chemical Physics 18, no. 8 (2016): 5720–28. http://dx.doi.org/10.1039/c5cp03044g.

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46

KUZEMSKY, A. L. "GENERALIZED KINETIC AND EVOLUTION EQUATIONS IN THE APPROACH OF THE NONEQUILIBRIUM STATISTICAL OPERATOR." International Journal of Modern Physics B 19, no. 06 (2005): 1029–59. http://dx.doi.org/10.1142/s0217979205029419.

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The method of the nonequilibrium statistical operator developed by D. N. Zubarev is employed to analyze and derive generalized transport and kinetic equations. The degrees of freedom in solids can often be represented as a few interacting subsystems (electrons, spins, phonons, nuclear spins, etc.). Perturbation of one subsystem may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between particles or with a thermal bath. The generalized kinetic equations were derived for a system weakly coupled to a thermal bath to elucidate the nature of tran

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47

Mohammed Djaouti, Abdelhamid. "Weakly Coupled System of Semi-Linear Fractional θ-Evolution Equations with Special Cauchy Conditions". Symmetry 15, № 7 (2023): 1341. http://dx.doi.org/10.3390/sym15071341.

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In this paper, we consider a weakly system of fractional θ-evolution equations. Using the fixed-point theorem, a global-in-time existence of small data solutions to the Cauchy problem is proved for one single equation. Using these results, we prove the global existence for the system under some mixed symmetrical conditions that describe the interaction between the equations of the system.

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48

Landim, Ricardo C. G. "Coupled tachyonic dark energy: A dynamical analysis." International Journal of Modern Physics D 24, no. 11 (2015): 1550085. http://dx.doi.org/10.1142/s0218271815500856.

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In this paper, we present a dynamical analysis for a coupled tachyonic dark energy with dark matter. The tachyonic field ϕ is considered in the presence of barotropic fluids (matter and radiation) and the autonomous system due to the evolution equations is studied. The three cosmological eras (radiation, matter and dark energy) are described through the critical points, for a generic potential V(ϕ).

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49

WEBB, G. M., M. BRIO, and G. P. ZANK. "Lagrangian and Hamiltonian aspects of wave mixing in non-uniform media: waves on strings and waves in gas dynamics." Journal of Plasma Physics 60, no. 2 (1998): 341–82. http://dx.doi.org/10.1017/s002237789800693x.

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Hamiltonian and Lagrangian perturbation theory is used to describe linear wave propagation in inhomogeneous media. In particular, the problems of wave propagation on an inhomogeneous string, and the propagation of sound waves and entropy waves in gas dynamics in one Cartesian space dimension are investigated. For the case of wave propagation on an inhomogeneous heavy string, coupled evolution equations are obtained describing the interaction of the backward and forward waves via wave reflection off gradients in the string density. Similarly, in the case of gas dynamics the backward and forward

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50

Borisov, V. E., A. V. Ivanov, B. V. Kritsky, and E. B. Savenkov. "Numerical Algorithms for Simulation of a Fluid-Filed Fracture Evolution in a Poroelastic Medium." PNRPU Mechanics Bulletin, no. 2 (December 15, 2021): 24–35. http://dx.doi.org/10.15593/perm.mech/2021.2.03.

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The paper deals with the computational framework for the numerical simulation of the three dimensional fluid-filled fracture evolution in a poroelastic medium. The model consists of several groups of equations including the Biot poroelastic model to describe a bulk medium behavior, Reynold’s lubrication equations to describe a flow inside fracture and corresponding bulk/fracture interface conditions. The geometric model of the fracture assumes that it is described as an arbitrary sufficiently smooth surface with a boundary. Main attention is paid to describing numerical algorithms for particul

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