Download or read book Well Posedness of the Cauchy Problem for n times n Systems of Conservation Laws written by Alberto Bressan and published by American Mathematical Soc.. This book was released on 2000 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and researchers interested in the mathematical physics and PDE.
Download or read book Well Posedness of the Cauchy Problem for N Times N Systems of Conservation written by Alberto Bressan and published by . This book was released on 2014-09-11 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and researchers interested in the mathematical physics and PDE.
Download or read book Well Posedness for General 2 times 2 Systems of Conservation Laws written by Fabio Ancona and published by American Mathematical Soc.. This book was released on 2004 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considers 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-linea
Download or read book Abstract Cauchy Problems written by Irina V. Melnikova and published by CRC Press. This book was released on 2001-03-27 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three major strategies for dealing with such problems: semigroup, abstract distribution, and regularizat
Download or read book Estimating the Error of Numerical Solutions of Systems of Reaction Diffusion Equations written by Donald J. Estep and published by American Mathematical Soc.. This book was released on 2000 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. In this paper, we outline, analyze, and test an approach to obtain computational error estimates based on the introduction of the residual error of the numerical solution and in which the effects of the accumulation of errors are estimated computationally. We begin by deriving an a posteriori relationship between the error of a numerical solution and its residual error using a variational argument. This leads to the introduction of stability factors, which measure the sensitivity of solutions to various kinds of perturbations. Next, we perform some general analysis on the residual errors and stability factors to determine when they are defined and to bound their size. Then we describe the practical use of the theory to estimate the errors of numerical solutions computationally. Several key issues arise in the implementation that remain unresolved and we present partial results and numerical experiments about these points. We use this approach to estimate the error of numerical solutions of nine standard reaction-diffusion models and make a systematic comparison of the time scale over which accurate numerical solutions can be computed for these problems. We also perform a numerical test of the accuracy and reliability of the computational error estimate using the bistable equation. Finally, we apply the general theory to the class of problems that admit invariant regions for the solutions, which includes seven of the main examples. Under this additional stability assumption, we obtain a convergence result in the form of an upper bound on the error from the a posteriori error estimate. We conclude by discussing the preservation of invariant regions under discretization.
Download or read book Frames Bases and Group Representations written by Deguang Han and published by American Mathematical Soc.. This book was released on 2000 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work develops an operator-theoretic approach to discrete frame theory on a separable Hilbert space. It is then applied to an investigation of the structural properties of systems of unitary operators on Hilbert space which are related to orthonormal wavelet theory. Also obtained are applications of frame theory to group representations, and of the theory of abstract unitary systems to frames generated by Gabor type systems.
Download or read book A Geometric Setting for Hamiltonian Perturbation Theory written by Anthony D. Blaom and published by American Mathematical Soc.. This book was released on 2001 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, the perturbation theory of non-commutatively integrable systems is revisited from the point of view of non-Abelian symmetry groups. Using a co-ordinate system intrinsic to the geometry of the symmetry, the book generalizes and geometrizes well-known estimates of Nekhoroshev (1977), in a class of systems having almost $G$-invariant Hamiltonians. These estimates are shown to have a natural interpretation in terms of momentum maps and co-adjoint orbits. The geometric framework adopted is described explicitly in examples, including the Euler-Poinsot rigid body.
Download or read book A New Construction of Homogeneous Quaternionic Manifolds and Related Geometric Structures written by Vicente Cortés and published by American Mathematical Soc.. This book was released on 2000 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $V = {\mathbb R}^{p,q}$ be the pseudo-Euclidean vector space of signature $(p,q)$, $p\ge 3$ and $W$ a module over the even Clifford algebra $C\! \ell^0 (V)$. A homogeneous quaternionic manifold $(M,Q)$ is constructed for any $\mathfrak{spin}(V)$-equivariant linear map $\Pi : \wedge^2 W \rightarrow V$. If the skew symmetric vector valued bilinear form $\Pi$ is nondegenerate then $(M,Q)$ is endowed with a canonical pseudo-Riemannian metric $g$ such that $(M,Q,g)$ is a homogeneous quaternionic pseudo-Kahler manifold. If the metric $g$ is positive definite, i.e. a Riemannian metric, then the quaternionic Kahler manifold $(M,Q,g)$ is shown to admit a simply transitive solvable group of automorphisms. In this special case ($p=3$) we recover all the known homogeneous quaternionic Kahler manifolds of negative scalar curvature (Alekseevsky spaces) in a unified and direct way. If $p>3$ then $M$ does not admit any transitive action of a solvable Lie group and we obtain new families of quaternionic pseudo-Kahler manifolds. Then it is shown that for $q = 0$ the noncompact quaternionic manifold $(M,Q)$ can be endowed with a Riemannian metric $h$ such that $(M,Q,h)$ is a homogeneous quaternionic Hermitian manifold, which does not admit any transitive solvable group of isometries if $p>3$. The twistor bundle $Z \rightarrow M$ and the canonical ${\mathrm SO}(3)$-principal bundle $S \rightarrow M$ associated to the quaternionic manifold $(M,Q)$ are shown to be homogeneous under the automorphism group of the base. More specifically, the twistor space is a homogeneous complex manifold carrying an invariant holomorphic distribution $\mathcal D$ of complex codimension one, which is a complex contact structure if and only if $\Pi$ is nondegenerate. Moreover, an equivariant open holomorphic immersion $Z \rightarrow \bar{Z}$ into a homogeneous complex manifold $\bar{Z}$ of complex algebraic group is constructed. Finally, the construction is shown to have a natural mirror in the category of supermanifolds. In fact, for any $\mathfrak{spin}(V)$-equivariant linear map $\Pi : \vee^2 W \rightarrow V$ a homogeneous quaternionic supermanifold $(M,Q)$ is constructed and, moreover, a homogeneous quaternionic pseudo-Kahler supermanifold $(M,Q,g)$ if the symmetric vector valued bilinear form $\Pi$ is nondegenerate.
Download or read book On the Connection between Weighted Norm Inequalities Commutators and Real Interpolation written by Jesús Bastero and published by American Mathematical Soc.. This book was released on 2001 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction Calderon weights Applications to real interpolation: reiteration and extrapolation Other classes of weights Extrapolation of weighted norm inequalities via extrapolation theory Applications to function spaces Commutators defined by the K-method Generalized commutators The quasi Banach case Applications to harmonic analysis BMO type spaces associated to Calderon weights Atomic decompositions and duality References.
Download or read book Analytic Quotients written by Ilijas Farah and published by American Mathematical Soc.. This book was released on 2000 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians interested in set theory.
Download or read book Maximum Entropy of Cycles of Even Period written by Deborah Martina King and published by American Mathematical Soc.. This book was released on 2001 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians interested in dynamical systems and ergodic theory.
Download or read book Equivariant Analytic Localization of Group Representations written by Laura Ann Smithies and published by American Mathematical Soc.. This book was released on 2001 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians interested in topological groups, Lie groups, category theory, and homological algebra.
Download or read book An Ergodic IP Polynomial Szemeredi Theorem written by Vitaly Bergelson and published by American Mathematical Soc.. This book was released on 2000 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors prove a polynomial multiple recurrence theorem for finitely many commuting measure preserving transformations of a probability space, extending a polynomial Szemerédi theorem appearing in [BL1]. The linear case is a consequence of an ergodic IP-Szemerédi theorem of Furstenberg and Katznelson ([FK2]). Several applications to the fine structure of recurrence in ergodic theory are given, some of which involve weakly mixing systems, for which we also prove a multiparameter weakly mixing polynomial ergodic theorem. The techniques and apparatus employed include a polynomialization of an IP structure theory developed in [FK2], an extension of Hindman's theorem due to Milliken and Taylor ([M], [T]), a polynomial version of the Hales-Jewett coloring theorem ([BL2]), and a theorem concerning limits of polynomially generated IP-systems of unitary operators ([BFM]).
Download or read book The Decomposition and Classification of Radiant Affine 3 Manifolds written by Suhyoung Choi and published by American Mathematical Soc.. This book was released on 2001 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: An affine manifold is a manifold with torsion-free flat affine connection - a geometric topologist would define it as a manifold with an atlas of charts to the affine space with affine transition functions. This title is an in-depth examination of the decomposition and classification of radiant affine 3-manifolds - affine manifolds of the type that have a holonomy group consisting of affine transformations fixing a common fixed point.
Download or read book Equivariant E Theory for C Algebras written by Erik Guentner and published by American Mathematical Soc.. This book was released on 2000 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title examines the equivariant e-theory for c*-algebra, focusing on research carried out by Higson and Kasparov. Let A and B be C*-algebras which are equipped with continuous actions of a second countable, locally compact group G. We define a notion of equivariant asymptotic morphism, and use it to define equivariant E-theory groups EULG(A, B) which generalize the E-theory groups of Connes and Higson. We develop the basic properties of equivariant E-theory, including a composition product and six-term exact sequences in both variables, and apply our theory to the problem of calculating K-theory for group C*-algebras. Our main theorem gives a simple criterion for the assembly map of Baum and Connes to be an isomorphism. The result plays an important role in the work of Higson and Kasparov on the Bau m-Connes conjecture for groups which act isometrically and metrically properly on Hilbert space
Download or read book On the Foundations of Nonlinear Generalized Functions I and II written by Michael Grosser and published by American Mathematical Soc.. This book was released on 2001 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: In part 1 of this title the authors construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces, previous attempts in this direction are unified and completed. Several classification results are achieved and applications to nonlinear differential equations involving singularities are given.
Download or read book On Natural Coalgebra Decompositions of Tensor Algebras and Loop Suspensions written by Paul Selick and published by American Mathematical Soc.. This book was released on 2000 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians interested in topology and representation theory.
