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Well-Posedness for General $2\times 2$ Systems of Conservation Laws - Fabio Ancona; Andrea Marson
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Fabio Ancona; Andrea Marson:
Well-Posedness for General $2\times 2$ Systems of Conservation Laws - First edition

2004, ISBN: 9780821834350

Paperback, Hardcover, ID: 333625417

New York : Norton, 1988., 1988. Book. Very Good. Hardcover. 1st Edition. 1st ed., 1st printing ; xvi, 361 p. : ill. ; 24 cm. ; ISBN: 0393024822 :; 9780393024821 LCCN: 87-7653 ; OCLC: 15366028 ; LC: QC21.2; Dewey: 530 ; Contents: Uniformity of Parts -- Rhapsody on JV The World Between -- Doppler Shift -- Three Ages -- Hi Transformations -- Ego and Survival -- Quantal Reality -- Radical Uniformity in Microcosm -- Transforming Principles -- Symmetry Lost and Symmetry Found -- Radical Uniformity in Macrocosm -- Quest -- Notes -- Index ; purple cloth with gold lettering in color pictorial dustjacket featuring painting, "The Metric System", by Pierre Roy ; "Devoted to sharing their own delight and awe before the fundamental mysteries of the cosmos, Frank Wilczek (winner of the 2004 Nobel Prize in Physics) and science writer Betsy Devine also have a serious purpose: to reveal to the lay reader how a heightened perception can respond to timeless themes of the physical universe. For example, they show that even the most exotic theories always confirm that physical laws are precisely the same throughout the universe, and they explain how we have learned that the most massive molten stars and the tiniest frozen particles are in physical harmony. In their descriptions of the workings of the half-known universe, Wilczek and Devine bring all of us face to face with the beauty of eternal order and the inevitability of rational ends and beginnings." ; FINE/FINE., New York : Norton, 1988., 1988, American Mathematical Society, 2004-05-01. Mass Market Paperback. New. Brand new. We distribute directly for the publisher. We consider the Cauchy problem for a strictly hyperbolic $2\times 2$ system of conservation laws in one space dimension $u_t+[F(u)]_x=0, u(0,x)=\bar u(x),$ which is neither linearly degenerate nor genuinely non-linear. We make the following assumption on the characteristic fields. If $r_i(u), \ i=1,2,$ denotes the $i$-th right eigenvector of $DF(u)$ and $\lambda_i(u)$ the corresponding eigenvalue, then the set $\{u : \nabla \lambda_i \cdot r_i (u) = 0\}$ is a smooth curve in the $u$-plane that is transversal to the vector field $r_i(u)$.Systems of conservation laws that fulfill such assumptions arise in studying elastodynamics or rigid heat conductors at low temperature.For such systems we prove the existence of a closed domain $\mathcal{D} \subset L^1,$ containing all functions with sufficiently small total variation, and of a uniformly Lipschitz continuous semigroup $S:\mathcal{D} \times [0,+\infty)\rightarrow \mathcal{D}$ with the following properties. Each trajectory $t \mapsto S_t \bar u$ of $S$ is a weak solution of (1). Viceversa, if a piecewise Lipschitz, entropic solution $u= u(t,x)$ of (1) exists for $t \in [0,T],$ then it coincides with the trajectory of $S$, i.e. $u(t,\cdot) = S_t \bar u.$This result yields the uniqueness and continuous dependence of weak, entropy-admissible solutions of the Cauchy problem (1) with small initial data, for systems satysfying the above assumption., American Mathematical Society, 2004-05-01

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Well-Posedness For General 2 X 2 Systems Of Conservation Laws
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Well-Posedness For General 2 X 2 Systems Of Conservation Laws - new book

ISBN: 9780821834350

ID: 6416379

We consider the Cauchy problem for a strictly hyperbolic $2 imes 2$ system of conservation laws in one space dimension $u t+[F(u)] x=0, u(0,x)= ar u(x),$ which is neither linearly degenerate nor genuinely non-linear. We make the following assumption on the characteristic fields. If $r i(u), i=1,2,$ denotes the $i$-th right eigenvector of $DF(u)$ and $lambda i(u)$ the corresponding eigenvalue. We consider the Cauchy problem for a strictly hyperbolic $2 imes 2$ system of conservation laws in one space dimension $u t+[F(u)] x=0, u(0,x)= ar u(x),$ which is neither linearly degenerate nor genuinely non-linear. We make the following assumption on the characteristic fields. If $r i(u), i=1,2,$ denotes the $i$-th right eigenvector of $DF(u)$ and $lambda i(u)$ the corresponding eigenvalue, then the set ${u: ; abla lambda i cdot r i (u) = 0}$ is a smooth curve in the $u$-plane that is transversal to the vector field $r i(u)$. Systems of conservation laws that fulfill such assumptions arise in studying elastodynamics or rigid heat conductors at low temperature. For such systems we prove the existence of a closed domain $mathcal{D} subset L^1,$ containing all functions with sufficiently small total variation, and of a uniformly Lipschitz continuous semigroup $S:mathcal{D} imes [0,+infty); ightarrow mathcal{D}$ with the following properties. Each trajectory $t mapsto S t ar u$ of $S$ is a weak solution of (1). Viceversa, if a piecewise Lipschitz, entropic solution $u= u(t,x)$ of (1) exists for $t in [0,T],$ then it coincides with the trajectory of $S$, i.e. $u(t,cdot) = S t ar u. This result yields the uniqueness and continuous dependence of weak, entropy-admissible solutions of the Cauchy problem with small initial data, for systems satysfying the above assumption. Books, Science and Geography~~Mathematics~~Calculus & Mathematical Analysis, Well-Posedness For General 2 X 2 Systems Of Conservation Laws~~Book~~9780821834350, , , , , , , , , ,, [PU: American Mathematical Society]

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Well-Posedness for General $2\\times 2$ Systems of Conservation Law - Fabio Ancona; Andrea Marson
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Fabio Ancona; Andrea Marson:
Well-Posedness for General $2\\times 2$ Systems of Conservation Law - Paperback

2004, ISBN: 0821834355

ID: 2717383383

[EAN: 9780821834350], Neubuch, [PU: American Mathematical Society], Brand new. We distribute directly for the publisher. We consider the Cauchy problem for a strictly hyperbolic $2\\times 2$ system of conservation laws in one space dimension $u_t+[F(u)]_x=0, u(0,x)=\\bar u(x),$ which is neither linearly degenerate nor genuinely non-linear. We make the following assumption on the characteristic fields. If $r_i(u), \\ i=1,2,$ denotes the $i$-th right eigenvector of $DF(u)$ and $\\lambda_i(u)$ the corresponding eigenvalue, then the set $\\{u : \\nabla \\lambda_i \\cdot r_i (u) = 0\\}$ is a smooth curve in the $u$-plane that is transversal to the vector field $r_i(u)$.Systems of conservation laws that fulfill such assumptions arise in studying elastodynamics or rigid heat conductors at low temperature.For such systems we prove the existence of a closed domain $\\mathcal{D} \\subset L^1,$ containing all functions with sufficiently small total variation, and of a uniformly Lipschitz continuous semigroup $S:\\mathcal{D} \\times [0,+\\infty)\\rightarrow \\mathcal{D}$ with the following properties. Each trajectory $t \\mapsto S_t \\bar u$ of $S$ is a weak solution of (1). Viceversa, if a piecewise Lipschitz, entropic solution $u= u(t,x)$ of (1) exists for $t \\in [0,T],$ then it coincides with the trajectory of $S$, i.e. $u(t,\\cdot) = S_t \\bar u.$This result yields the uniqueness and continuous dependence of weak, entropy-admissible solutions of the Cauchy problem (1) with small initial data, for systems satysfying

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Well-posedness for General 2 X 2 Systems of Conservation Laws (Paperback)
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Well-posedness for General 2 X 2 Systems of Conservation Laws (Paperback) - Paperback

2004, ISBN: 0821834355

ID: 11234693754

[EAN: 9780821834350], Neubuch, [PU: American Mathematical Society, United States], Brand New Book. We consider the Cauchy problem for a strictly hyperbolic $2 times 2$ system of conservation laws in one space dimension $u t+[F(u)] x=0, u(0,x)= ar u(x),$ which is neither linearly degenerate nor genuinely non-linear. We make the following assumption on the characteristic fields. If $r i(u), i=1,2,$ denotes the $i$-th right eigenvector of $DF(u)$ and $ lambda i(u)$ the corresponding eigenvalue, then the set $ {u: nabla lambda i cdot r i (u) = 0 }$ is a smooth curve in the $u$-plane that is transversal to the vector field $r i(u)$. Systems of conservation laws that fulfill such assumptions arise in studying elastodynamics or rigid heat conductors at low temperature.For such systems we prove the existence of a closed domain $ mathcal{D} subset L^1,$ containing all functions with sufficiently small total variation, and of a uniformly Lipschitz continuous semigroup $S: mathcal{D} times [0,+ infty) rightarrow mathcal{D}$ with the following properties. Each trajectory $t mapsto S t ar u$ of $S$ is a weak solution of (1). Viceversa, if a piecewise Lipschitz, entropic solution $u= u(t,x)$ of (1) exists for $t in [0,T],$ then it coincides with the trajectory of $S$, i.e. $u(t, cdot) = S t ar u. This result yields the uniqueness and continuous dependence of weak, entropy-admissible solutions of the Cauchy problem with small initial data, for systems satysfying the above assumption.

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Well-posedness for General 2 X 2 Systems of Conservation Laws - Fabio Ancona; Andrea Marson
book is out-of-stock
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Fabio Ancona; Andrea Marson:
Well-posedness for General 2 X 2 Systems of Conservation Laws - Paperback

2004, ISBN: 9780821834350

ID: 5988066

Softcover, Buch, [PU: American Mathematical Society]

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