Relevant bibliographies by topics / Initial-boundary value problem for balance laws

Academic literature on the topic 'Initial-boundary value problem for balance laws'

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Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Initial-boundary value problem for balance laws"

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Gugat, Martin, and Stefan Ulbrich. "Lipschitz solutions of initial boundary value problems for balance laws." Mathematical Models and Methods in Applied Sciences 28, no. 05 (May 2018): 921–51. http://dx.doi.org/10.1142/s0218202518500240.

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The flow of gas through networks of pipes can be modeled by the isothermal Euler equations and algebraic node conditions that model the flow through the vertices of the network graph. This motivates our analysis of the well-posedness of a coupled system of [Formula: see text] conservation laws on a network. We consider initial data and control functions that are Lipschitz continuous and compatible with the node and boundary conditions. We show the existence of semi-global Lipschitz continuous solutions of the initial boundary value problem on a network. The construction of the solution is based upon a fixed point iteration along the characteristic curves. The solutions of the initial boundary value problem on arbitrary networks satisfy a maximum principle in terms of the Riemann invariants that states that the maximum of the absolute values is attained for the initial or the boundary data.
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Chou, Shih-Wei, John M. Hong, and Ying-Chin Su. "The initial-boundary value problem of hyperbolic integro-differential systems of nonlinear balance laws." Nonlinear Analysis: Theory, Methods & Applications 75, no. 15 (October 2012): 5933–60. http://dx.doi.org/10.1016/j.na.2012.06.006.

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Hong, John M., and Ying-Chin Su. "Generalized Glimm scheme to the initial boundary value problem of hyperbolic systems of balance laws." Nonlinear Analysis: Theory, Methods & Applications 72, no. 2 (January 2010): 635–50. http://dx.doi.org/10.1016/j.na.2009.07.003.

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Rossi, Elena. "Well-posedness of general 1D initial boundary value problems for scalar balance laws." Discrete & Continuous Dynamical Systems - A 39, no. 6 (2019): 3577–608. http://dx.doi.org/10.3934/dcds.2019147.

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Rossi, Elena. "Definitions of solutions to the IBVP for multi-dimensional scalar balance laws." Journal of Hyperbolic Differential Equations 15, no. 02 (June 2018): 349–74. http://dx.doi.org/10.1142/s0219891618500133.

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We consider four definitions of solution to the initial-boundary value problem (IBVP) for a scalar balance laws in several space dimensions. These definitions are extended to the same most general framework and then compared. The first aim of this paper is to detail differences and analogies among them. We focus then on the ways the boundary conditions are fulfilled according to each definition, providing also connections among these various modes. The main result is the proof of the equivalence among the presented definitions of solution.
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Li, Huicong, and Kun Zhao. "Initial–boundary value problems for a system of hyperbolic balance laws arising from chemotaxis." Journal of Differential Equations 258, no. 2 (January 2015): 302–38. http://dx.doi.org/10.1016/j.jde.2014.09.014.

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Galeş, C. "A Mixture Theory for Micropolar Thermoelastic Solids." Mathematical Problems in Engineering 2007 (2007): 1–21. http://dx.doi.org/10.1155/2007/90672.

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We derive a nonlinear theory of heat-conducting micropolar mixtures in Lagrangian description. The kinematics, balance laws, and constitutive equations are examined and utilized to develop a nonlinear theory for binary mixtures of micropolar thermoelastic solids. The initial boundary value problem is formulated. Then, the theory is linearized and a uniqueness result is established.
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Feng, Zefu. "Initial and Boundary Value Problem for a System of Balance Laws from Chemotaxis: Global Dynamics and Diffusivity Limit." Annals of Applied Mathematics 37, no. 1 (June 2021): 61–110. http://dx.doi.org/10.4208/aam.oa-2020-0004.

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Passarella, Francesca, and Vincenzo Tibullo. "Uniqueness of Solutions in Thermopiezoelectricity of Nonsimple Materials." Entropy 24, no. 9 (September 1, 2022): 1229. http://dx.doi.org/10.3390/e24091229.

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This article presents the theory of thermopiezoelectricity in which the second displacement gradient and the second electric potential gradient are included in the set of independent constitutive variables. This is achieved by using the entropy production inequality proposed by Green and Laws. At first, appropriate thermodynamic restrictions and constitutive equations are obtained, using the well-established Coleman and Noll procedure. Then, the balance equations and the constitutive equations of linear theory are derived, and the mixed initial-boundary value problem is set. For this problem a uniqueness result is established. Next, the basic equations for the isotropic case are derived. Finally, a set of inequalities is obtained for the constant constitutive coefficients of the isotropic case that, on the basis on the previous theorem, ensure the uniqueness of the solution of the mixed initial-boundary value problem.
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Hong, John Meng-Kai, and Reyna Marsya Quita. "Approximation of generalized Riemann solutions to compressible Euler-Poisson equations of isothermal flows in spherically symmetric space-times." Tamkang Journal of Mathematics 48, no. 1 (March 30, 2017): 73–94. http://dx.doi.org/10.5556/j.tkjm.48.2017.2274.

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In this paper, we consider the compressible Euler-Poisson system in spherically symmetric space-times. This system, which describes the conservation of mass and momentum of physical quantity with attracting gravitational potential, can be written as a $3\times 3$ mixed-system of partial differential systems or a $2\times 2$ hyperbolic system of balance laws with $global$ source. We show that, by the equation for the conservation of mass, Euler-Poisson equations can be transformed into a standard $3\times 3$ hyperbolic system of balance laws with $local$ source. The generalized approximate solutions to the Riemann problem of Euler-Poisson equations, which is the building block of generalized Glimm scheme for solving initial-boundary value problems, are provided as the superposition of Lax's type weak solutions of the associated homogeneous conservation laws and the perturbation terms solved by the linearized hyperbolic system with coefficients depending on such Lax solutions.
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Dissertations / Theses on the topic "Initial-boundary value problem for balance laws"

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ROSSI, ELENA. "Balance Laws: Non Local Mixed Systems and IBVPs." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2016. http://hdl.handle.net/10281/103090.

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Scalar hyperbolic balance laws in several space dimensions play a central role in this thesis. First, we deal with a new class of mixed parabolic-hyperbolic systems on all R^n: we obtain the basic well-posedness theorems, devise an ad hoc numerical algorithm, prove its convergence and investigate the qualitative properties of the solutions. The extension of these results to bounded domains requires a deep understanding of the initial boundary value problem (IBVP) for hyperbolic balance laws. The last part of the thesis provides rigorous estimates on the solution to this IBVP, under precise regularity assumptions. In Chapter 1 we introduce a predator-prey model. A non local and non linear balance law is coupled with a parabolic equation: the former describes the evolution of the predator density, the latter that of prey. The two equations are coupled both through the convective part of the balance law and the source terms. The drift term is a non local function of the prey density. This allows the movement of predators to be directed towards the regions where the concentration of prey is higher. We prove the well-posedness of the system, hence the existence and uniqueness of solution, the continuous dependence from the initial data and various stability estimates. In Chapter 2 we devise an algorithm to compute approximate solutions to the mixed system introduced above. The balance law is solved numerically by a Lax-Friedrichs type method via dimensional splitting, while the parabolic equation is approximated through explicit finite-differences. Both source terms are integrated by means of a second order Runge-Kutta scheme. The key result in Chapter 2 is the convergence of this algorithm. The proof relies on a careful tuning between the parabolic and the hyperbolic methods and exploits the non local nature of the convective part in the balance law. This algorithm has been implemented in a series of Python scripts. Using them, we obtain information about the possible order of convergence and we investigate the qualitative properties of the solutions. Moreover, we observe the formation of a striking pattern: while prey diffuse, predators accumulate on the vertices of a regular lattice. The analytic study of the system above is on all R^n. However, both possible biological applications and numerical integrations suggest that the boundary plays a relevant role. With the aim of studying the mixed hyperbolic-parabolic system in a bounded domain, we noticed that for balance laws known results lack some of the estimates necessary to deal with the coupling. In Chapter 3 we then focus on the IBVP for a general balance law in a bounded domain. We prove the well-posedness of this problem, first with homogeneous boundary condition, exploiting the vanishing viscosity technique and the doubling of variables method, then for the non homogeneous case, mainly thanks to elliptic techniques. We pay particular attention to the regularity assumptions and provide rigorous estimates on the solution.
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Schmitt, Johann Michael [Verfasser]. "Optimal Control of Initial-Boundary Value Problems for Hyperbolic Balance Laws with Switching Controls and State Constraints / Johann Michael Schmitt." München : Verlag Dr. Hut, 2019. http://d-nb.info/1188516450/34.

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Book chapters on the topic "Initial-boundary value problem for balance laws"

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Nolte, M., and D. Kröner. "Convergence of Well-Balanced Schemes for the Initial Boundary Value Problem for Scalar Conservation Laws in 1D." In Hyperbolic Problems: Theory, Numerics, Applications, 791–98. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-75712-2_81.

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Anand, Lallit, and Sanjay Govindjee. "Variational formulation of boundary-value problems." In Continuum Mechanics of Solids, 215–22. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198864721.003.0010.

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This chapter discusses a variational formulation of boundary value problems in small deformation solid mechanics. It begins by introducing the important principle of virtual power, and shows that it encapsulates Cauchy’s traction law, and the local form of the basic balance of forces (equation of equilibrium), and the local from of the balance of moments (symmetry of the stress). Since the principle of virtual power encapsulates both the equation of equilibrium and the Cauchy relation for tractions, it can be used to formulate and solve boundary-value problems in solid mechanics in a variational or weak sense. Specifically, it is shown how the displacement problem of linear elastostatics may be formulated variationally using the principle of virtual power.
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Conference papers on the topic "Initial-boundary value problem for balance laws"

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Pournazeri, Mohammad, Amir Fazeli, and Amir Khajepour. "A Robust Lift Control Technique in Electro-Hydraulic Camless Valves Using System Average Model." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-38691.

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In electro-hydraulic camless valvetrains, both valve timing and lift are simultaneously controlled through precise control of solenoid actuated servo-valves at each cycle. In fact, the desired maximum lift is obtained by accurate controlling of the servo-valve opening interval. However, at high engine speeds, due to the slow servo-valve response time, concurrent control of both timing and peak lift becomes more difficult and sometimes impossible. In this paper a new valve lift control technique is proposed based on the average model of the mechanism introduced in [1]. Using this method, it is possible to control the valve lift without precise control of the high pressure servo-valve opening interval and the servo-valves are only responsible for controlling the valve timings and duration. This eliminates the need for high precision servo-valves and measuring devices and consequently cut the system cost. In contrast to the existing lift control methods in which the maximum lift should be repeatedly controlled within each cycle, employing this technique, it is possible to adjust the maximum valve lift after few engine cycles. To this end, an average model of the system is developed based on system energy balance and a non-linear sliding mode controller is designed and implemented on the proposed mechanism. To compensate for the model uncertainties, the designed sliding mode controller is equipped with adaptive law. A conventional boundary layer method is used to solve the controller chattering problem. Finally, the performance of the proposed lift control technique is evaluated through simulation.
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Machado, Margarida, and Paulo Flores. "A Novel Continuous Contact Force Model for Multibody Dynamics." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47086.

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A general and comprehensive analysis on the continuous contact force models in multibody dynamics is presented and a novel contact force model is proposed. The force models are developed based on the foundation of the Hertz law together with a hysteresis damping parameter that accounts for the energy dissipation during the contact process. In a simple way, these contact force models are based on the analysis and development of three main issues: (i) the dissipated energy associated with the coefficient of restitution that includes the balance of kinetic energy and the conservation of the linear momentum between the initial and final instant of contact; (ii) the stored elastic energy, representing part of initial kinetic energy, which is evaluated as the work done by the contact force developed during the contact process; (iii) the dissipated energy due to internal damping, which is evaluated by modeling the contact process as a single degree-of-freedom system to obtain a hysteresis damping factor. This factor takes into account the geometrical and material properties, as well as the kinematic characteristics of the contacting bodies. The proposed contact force model has the great merit that can be used for contact problems involving materials with low or moderate values of coefficient of restitution. This contact force model is suitable to be included into the equations of motion of a multibody system and contributes to their stable numerical resolution. Two demonstrative examples of application are used to provide the results that support the analysis and discussion of procedures and methodologies adopted in this work.
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