Temat: conservation laws - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Embedded Solitons and Conservation Law with $χ^{(2)}$ and $χ^{(3)}$ Nonlinear Susceptibilities
Autorzy:: Savescu, M.
Kara, A.
Kumar, S.
Krishnan, E.
Zaka Ullah, M.
Moshokoa, S.
Zhou, Qin
Biswas, A.
Tematy:: solitons
χ^{(2)}
conservation laws; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Fizyki PAN
Powiązania:: https://bibliotekanauki.pl/articles/1398312.pdf Link otwiera się w nowym oknie
Opis:: This paper studies embedded solitons that are confined to continuous spectrum, with $χ^{(2)}$ and $χ^{(3)}$ nonlinear susceptibilities. Bright and singular soliton solutions are obtained by the method of undetermined coefficients. Subsequently, the Lie symmetry analysis and mapping method retrieves additional solutions to the model such as shock waves, singular solitons, cnoidal waves, and several others. Finally, a conservation law for this model is secured through the Lie symmetry analysis.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Global existence for strong solutions of viscous Burgers equation. (1) The bounded case
Autorzy:: Unterberger, J.
Tematy:: viscous Burgers equation
conservation laws
maximum principle
Schauder estimates; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/206077.pdf Link otwiera się w nowym oknie
Opis:: We prove that the viscous Burgers equation (∂t−∆)u(t, x)+( u •∇)u(t, x) = g(t, x), (t, x) ∈ R+ × Rd (d ≥ 1) has a globally deﬁned smooth solution in all dimensions provided the initial condition and the forcing term g are smooth and bounded together with their derivatives. Such solutions may have inﬁnite energy. The proofdoes not rely on energy estimates, but on a combinationof the maximumprinciple and quantitative Schauder estimates. We obtain precise bounds on the sup norm of the solution and its derivatives, making it plain that there is no exponential increase in time. In particular, these bounds are time-independent if g is zero. To get a classical solution, it suﬃces to assume that the initial condition and the forcing term have bounded derivatives up to order two.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Conservation Laws in Physics. Emmy Noether’s Theorem
Autorzy:: Manolea, D.
Tematy:: practical character of physics
conservation laws
Emmy Noerther’s Theorem; Pokaż więcej
Wydawca:: Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Powiązania:: https://bibliotekanauki.pl/articles/412434.pdf Link otwiera się w nowym oknie
Opis:: The study is explanatory-interpretative and argues the practical character of Physics. It starts from premise that formation of a correct conception of the world begins with the understanding of physics. It is one of the earliest chapters of human knowledge, studying the material world from the microscopic level of the particles to the macroscopic level of the celestial body. As an example for the practical importance of applying the laws of physics take the set of physical laws of conservation, in particular, it explains the practical impact of Emmy Noether's Theorem.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: $L^p$-decay of solutions to dissipative-dispersive perturbations of conservation laws
Autorzy:: Karch, Grzegorz
Tematy:: asymptotic behavior of solutions
dispersive equations
parabolic conservation laws
oscillatory integrals; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Powiązania:: https://bibliotekanauki.pl/articles/1294727.pdf Link otwiera się w nowym oknie
Opis:: We study the decay in time of the spatial $L^p$-norm (1 ≤ p ≤ ∞) of solutions to parabolic conservation laws with dispersive and dissipative terms added uₜ - uₓₓₜ - νuₓₓ + buₓ = f(u)ₓ or uₜ + uₓₓₓ - νuₓₓ + buₓ = f(u)ₓ, and we show that under general assumptions about the nonlinearity, solutions of the nonlinear equations have the same long time behavior as their linearizations at the zero solution.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: On the numerical discretization of optimal control problems for conservation laws
Autorzy:: Schäfer Aguilar, Paloma
Schmitt, Johann Michael
Ulbrich, Stefan
Moos, Michael
Tematy:: conservation laws
adjoint state
linear transport equation
discontinuous coefficients
finite difference schemes; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/1839148.pdf Link otwiera się w nowym oknie
Opis:: We analyze the convergence of discretization schemes for the adjoint equation arising in the adjoint-based derivative computation for optimal control problems governed by entropy solutions of conservation laws. The difficulties arise from the fact that the correct adjoint state is the reversible solution of a transport equation with discontinuous coefficient and discontinuous end data. We derive the discrete adjoint scheme for monotone difference schemes in conservation form. It is known that convergence of the discrete adjoint can only be expected if the numerical scheme has viscosity of order O(h) with appropriate 0 < α < 1, which leads to quite viscous shock profiles. We show that by a slight modification of the end data of the discrete adjoint scheme, convergence to the correct reversible solution can be obtained also for numerical schemes with viscosity of order O(h) and with sharp shock resolution. The theoretical findings are confirmed by numerical results.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 6.

Tytuł:: Balance errors in numerical solutions of shallow water equations
Autorzy:: Gąsiorowski, D.
Tematy:: shallow water equations
nonlinear advection equations
numerical errors
conservation laws
mass and momentum balance; Pokaż więcej
Wydawca:: Politechnika Gdańska
Powiązania:: https://bibliotekanauki.pl/articles/1933150.pdf Link otwiera się w nowym oknie
Opis:: An analysis of the conservative properties of shallow water equations is presented, focused on the consistency of their numerical solution with the conservation laws of mass and momentum. Two different conservative forms are considered, solved by an implicit box scheme. Theoretical analysis supported with numerical experiments is carried out for a rectangular channel and arbitrarily assumed flow conditions. The improper conservative form of the dynamic equation is shown not to guarantee a correct solution with respect to the conservation of momentum. Consequently, momentum balance errors occur in the numerical solution. These errors occur when artificial diffusion is simultaneously generated by a numerical algorithm.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 7.

Tytuł:: Thermal waves, second sound - work of Witold Kosiński
Autorzy:: Saxton, Katarzyna
Saxton, Ralph
Tematy:: continuum thermodynamics, nonlinear waves, singularities, conservation laws
mechanika ośrodków ciągłych, fale nieliniowe, osobliwości, prawa zachowania; Pokaż więcej
Wydawca:: Polskie Towarzystwo Matematyczne
Powiązania:: https://bibliotekanauki.pl/articles/748082.pdf Link otwiera się w nowym oknie
Opis:: Niniejsza praca jest poswięcona pamięci naszego przyjaciela Witolda Kosińskego. Chcielibysmy przedstawić jego najważniejsze osiągnięcia w dziedzine propagacji fal termicznych, termodynamiki i teorii hiperbolicznych ukladów rózniczkowych. Zakres badań Kosińskiego był bardzo bogaty. Obejmował wiele dyscyplin na pograniczu mechaniki, matematyki i teorii komputerowych. Współpraca z Witoldem była owocna, zawsze wypełniona entuzjazmem i wzajemnym szacunkiem. Autorzy tego artykułu jak i inni współpracownicy Witolda korzystali z jego wiedzy i zawodowego doświadczenia. Będzie nam go bardzo brakowało.
This paper is dedicated to Witold Kosinski. Our contribution to this special issue will concentrate on the properties of thermal waves, one of many scientic interests of our friend and collaborator, and this article is dedicated to his memory. Working together with Witold was always an insightful and very pleasant experience, and it beneted all of his coworkers including the authors of this note. His scope of research was broad, spanningmany disciplines and applications. Here we focus on a few of those aspects to which he applied a deep knowledge of continuum thermodynamics and its mathematical foundations.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 8.

Tytuł:: Isospectral integrability analysis of dynamical systems on discrete manifolds
Autorzy:: Blackmore, D.
Prykarpatsky, A. K.
Prykarpatsky, Y. A.
Tematy:: gradient holonomic algorithm
conservation laws
asymptotic analysis
Poissonian structures
Lax representation
finite dimensional reduction
Liouville integrability
nonlinear discrete dynamical systems; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/255384.pdf Link otwiera się w nowym oknie
Opis:: It is shown how functional-analytic gradient-holonomic structures can be used for an isospectral integrability analysis of nonlinear dynamical systems on discrete manifolds. The approach developed is applied to obtain detailed proofs of the integrability of the discrete nonlinear Schrödinger, Ragnisco-Tu and Riemann-Burgers dynamical systems.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 9.

Tytuł:: Kinetic-induced moment systems for the Saint-Venant equations
Autorzy:: Gil Montoya, D. C.
Struckmeier, J.
Tematy:: Saint-Venant equations
shallow water equations
Boltzmann equation
hyperbolic conservation laws
kinetic models
kinetic representations
relaxion systems
shock waves
rarefaction waves; Pokaż więcej
Wydawca:: Politechnika Gdańska
Powiązania:: https://bibliotekanauki.pl/articles/1933941.pdf Link otwiera się w nowym oknie
Opis:: Based on the relation between kinetic Boltzmann-like transport equations and nonlinear hyperbolic conservation laws, we derive kinetic-induced moment systems for the spatially one-dimensional shallow water equations (the Saint-Venant equations). Using Chapman-Enskog-like asymptotic expansion techniques in terms of the relaxation parameter of the kinetic equation, the resulting moment systems are asymptotically closed without the need for an additional closure relation. Moreover, the new second order moment equation for the (asymptotically) third order system may act as a monitoring function to detect shock and rarefaction waves, which we confirm by a number of numerical experiments.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 10.

Tytuł:: Systems of conservation laws with discontinuous fluxes and applications to traffic
Autorzy:: Rosini, Massimiliano
Tematy:: Conservation laws
Aw-Rascle-Zhang model for vehicular traffic
discontinuous flux
follow-the-leader model
Riemann solvers
point constraint on the flux
point constraint on the velocity; Pokaż więcej
Wydawca:: Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Powiązania:: https://bibliotekanauki.pl/articles/1395936.pdf Link otwiera się w nowym oknie
Opis:: In this paper we study $2\times 2$ systems of conservation laws with discontinuous fluxes arising in vehicular traffic modeling. The main goal is to introduce an appropriate notion of solution. To this aim we consider physically reasonable microscopic follow-the-leader models. Macroscopic Riemann solvers are then obtained as many particle limits. This approach leads us to develop six models. We propose a unified way to describe such models, which highlights their common property of maximizing the density flow across the interface under appropriate physical restrictions depending on the case at hand.
Dostawca treści:: Biblioteka Nauki

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