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Untitled Document From a perspective of applied analysis, members of the team are interested in the theory of conservation laws, the theory of Hamilton-Jacobi equations, and the theory of collisional kinetic models as they arise in dilute gases and in radiative transport. The group is interested in modeling, analysis and the development of computational methods for nonlinear wave hyperbolic and dispersive waves arising in a variety of applications from fluid dynamics, kinetic theory, material science, mathematical biology and geophysics. There is an ongoing activity on numerical methods for the equations of fluid mechanics, icluding Navier Stokes, shallow water wave equations and gas dynamics. www.iacm.forth.gr /wave/nlwp/nonlinearwp.htm   (247 words)

Web server of HYKE /team.php The group has extensive experience in the theory of conservation laws and Hamilton-Jacobi equations and the interface of hyperbolic and kinetic problems, with ongoing collaborations with the teams (F1, F2, F3, I1, I2). The research interests of the group are in Theoretical Mechanics, Theory of Conservation Laws, Theory of Hamilton-Jacobi equations, and development of modeling and computational methods for these problems. There are collaborations with the teams F2, S2 on issues related to convergence and properties of finite difference and finite volume schemes, the kinetic formulation of classical schemes, and numerical approximations of stochastic equations. www.hyke.org /team.php?t=G1   (477 words)

Global-Investor Bookshop : Partial Differential Equations by Lawrence C. Evans Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and much more. The exposition is divided into three parts: 1) representation formulas for solutions, 2) theory for linear partial differential equations, and 3) theory for nonlinear partial differential equations. Generally the approach of the author is to explain the fundamental ideas of a subject in a clearest possible setting, and to emphasize the importance of nonlinear concepts and of generalized solutions. books.global-investor.com /books/20444.htm?ginPtrCode=00000   (690 words)

Optimal Soaring -- Robert Almgren / Agnes Tourin This nonlinear Hamilton-Jacobi-Bellman equation is surprisingly difficult to solve numerically, but techniques based on the theory of viscosity solutions give very good methods (see Barles and Souganidis 1991)). We address the problem of uncertain future atmospheric conditions by constructing a nonlinear Hamilton-Jacobi-Bellman equation for the optimal speed to fly, with a free boundary describing the climb/cruise decision. Barles (1997), Convergence of numerical schemes for degenerate parabolic equations arising in finance theory, in Numerical Methods in Finance, L. Rogers and D. Talay, eds., Cambridge University Press, pp. www.math.toronto.edu /almgren/optsoar   (2784 words)

Syllabus for Math 496, Spring 1997 Hamilton-Jacobi-Bellman) equations: existence and uniqueness of solutions; relations to stochastic control theory and mathematical finance. Hamilton-Jacobi equations: the method of characteristics; Hopf's formula for weak solutions; a little convex analysis. We will carry out a detailed study of several classes of nonlinear PDE, including equations which are widely used in various fields of applied mathematics, such as mathematical physics, deterministic and stochastic control theory, and mathematical finance. www.math.uiuc.edu /~rjerrard/496/oldsyl.html   (206 words)

Resume Wizard A substantial background in mathematics, numerical analysis, differential equations, mathematical modeling, image processing, computational and applied mathematics, probability theory and stochastic processes. Theory of Partial Differential Equations I and II. The method introduces a completely new idea to generate an adaptive mesh by a self-adaptive algorithm that guarantees a strict error control. www.math.umn.edu /~yenikaya/aboutme/MyResume.htm   (358 words)

Hamilton-Jacobi-Bellman equation The Hamilton-Jacobi-Bellman (HJB) equation is a partial differential equation which is central to optimal control theory. The equation is a result of the theory of dynamic programming which was pioneered in the 1950s by Richard Bellman and coworkers. The corresponding discrete-time equation is usually referred to as the Bellman equation. www.worldhistory.com /wiki/H/Hamilton-Jacobi-Bellman-equation.htm   (241 words)

SSRN-Perturbative Solutions of Hamilton Jacobi Bellman Equations in Robust Decision Making by Fabio Trojani, Paolo Vanini Keywords: Hamilton-Jacobi Bellman Equations, Model Misspecification, Perturbation Theory, Robust Decision Making Trojani, Fabio and Vanini, Paolo, "Perturbative Solutions of Hamilton Jacobi Bellman Equations in Robust Decision Making" (April 2002). SSRN-Perturbative Solutions of Hamilton Jacobi Bellman Equations in Robust Decision Making by Fabio Trojani, Paolo Vanini papers.ssrn.com /sol3/papers.cfm?abstract_id=311821   (203 words)

Willard Miller: Bibliography The theory of orthogonal R-separation for Helmholtz equations, with E.G. Kalnins, Advances in Mathematics, 51 (1984), pp. Matrix operator symmetries of the Dirac equation and separation of variables, with E.G. Kalnins and G.C. Williams, J. Math. Separability of wave equations, with E.G. Kalnins and G.C. Williams, 33-51, in ``Black Holes, Gravitational Radiation and the Universe, Essays in honor of C.V. Vishveshwara'', B.R. Iyer and B. Bhawal, eds., Kluwer Academic Publishers, Dordrecht, 1999. www.ima.umn.edu /%7Emiller/bibli.html   (2960 words)

I S T :: Information Science and Technology :: M A S T E R - C A L E N D A R Hamilton-Jacobi equations arise in a huge variety of contexts. Such models, although quite crude, are useful in solid combustion engineering: it is indeed very difficult to devise a good burning rate theory in the context of solid combustion. The specific problem of the time-asymptotic behaviour of their solutions came up as a solid combustion problem, namely the propagation of a flame front in a solid medium, governed by a non-homogeneous eikonal equation. today.caltech.edu /eas/item?calendar_id=51887&template=ist-all   (132 words)

Georgia Tech School of Mathematics: Seminars We present a method, based on Conley index theory, that insures the existence of an equilibrium of a time dependent equation in a computed neighborhood. By using center manifold and normal form reductions, we show that a continuous NLS equation with the third-order derivative term is a canonical normal form for the discrete NLS equation near the zero-dispersion limit. The Cahn-Hilliard equation, a parabolic equation of fourth order, was introduced as a model for the process of phase separation of a binary alloy at a fixed temperature. www.math.gatech.edu /news/seminars   (1353 words)

Livre Semiconcave functions, Hamilton-Jacobi equations, and optimal control - P. Cannarsa, C. Sinestrari - - Librairie Eyrolles This text is the first comprehensive exposition of the theory of semiconcave functions, and of the role they play in optimal control and Hamilton-Jacobi equations. Semiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider range of applications. equations, and finally analyzed in connection with optimal trajectories of control systems. www.eyrolles.com /Informatique/Livre/9780817640842/livre-semiconcave-functions-hamilton-jacobi-equations-and-optimal-control.php?societe=devasso   (322 words)

TEL :: CONSULTER We use the same techniques to prove the existence of a minimal lsc solution for Hamilton-Jacobi equations under weaker assumptions than the ones found in the traditional viscosity solution theory. The last part is devoted to the construction of a lower semicontinuous solution of a Hamilton-Jacobi equation whose hamiltonian is the supremum of a parametric family of hamiltonians H(x,u,p) that are convex in p. It is therefore satisfactory to prove that the support function of the generalized jacobian is a ``generalized directional divergence''. tel.ccsd.cnrs.fr /documents/archives0/00/00/12/03/index_fr.html   (779 words)

Diogo Aguiar Gomes Homepage Perturbation theory for Hamilton-Jacobi equations and stability of Aubry-Mather sets, accepted for publication in the SIAM journal of Mathematical Analysis. Duality principles for fully-nonlinear elliptic equations, accepted for publication in Progress in Nonlinear Differential Equations and Their Applications, Vol. Convergence of Viscosity Solutions of Burgers equations with Random Forcing, with R. Iturriaga, K. Khanin, and P. Padilla, submitted for publication. www.math.ist.utl.pt /%7Edgomes   (789 words)

Doron Levy (publications) The derivation of the new equations uses a Pade (2,2) approximation of the phase velocity that arises in the linear water wave theory. The dynamics of the atmosphere is modeled with the Euler equations in a variable-sized flux tube in the presence of gravity. We analyze self-focusing and singularity formation in the complex Ginzburg-Landau equation (CGL) in the regime where it is close to the critical nonlinear Schrodinger equation. math.stanford.edu /~dlevy/pub.html   (5772 words)

Takasaki's Recent Papers and Articles Abstract The hierarchy structure associated with a (2+1)-dimensional Nonlinear Schroedinger equation is discussed as an extension of the theory of the KP hierarchy. In this paper, we present a result on the Hamiltonian structure of this equation in the case where Q is of second order and P of odd (2g + 1) order. Abstract The Landau-Lifshitz equation is known to have a Lax representation with matrices depending on a spectral parameter on the torus. www.math.h.kyoto-u.ac.jp /~takasaki/res/recent-e.html   (5304 words)

mp_arc 01-423 Regularity Theory for Hamilton-Jacobi Equations (280K, pdf) Nov 14, 01 The objective of this paper is to discuss the regularity of viscosity solutions of time independent Hamilton-Jacobi Equations. We prove analogs of the KAM theorem, show stability of the viscosity solutions and Mather sets under small perturbations of the Hamiltonian. www.ma.utexas.edu /mp_arc-bin/mpa?yn=01-423   (50 words)

20a An example of such extensions are the stochastic Mather measures which can be used to analyze second order Hamilton-Jacobi equations. is equivalent to the existence of regular solutions of the Hamilton-Jacobi equation (Takis Souganidis) Homogenization problem for random Hamilton-Jacobi equation www.aimath.org /WWN/dynpde/articles/html/20a   (1307 words)

Evolution Equations A characterization of the value function by an appropriate Hamilton Jacobi Bellman equation (in viscosity sense) is obtained and optimality conditions are derived. In the theory of invariant measures for stochastic evolution equations in Hilbert spaces, results on and examples of invariant measures for equations with unstable drift semigroups are sparse. The controllability of finite-level Schrodinger equation was intensively investigated in the last years but the proper infinite-dimensional case was not studied at all. fraise.univ-brest.fr /~eveq/results.html   (7508 words)

Hamilton-Jacobi-Bellman Equation The HJB equation is a central result in optimal control theory. Many other principles and design techniques follow from the HJB equation, which itself is just a statement of the dynamic programming principle in continuous time. A proper derivation of all forms of the HJB equation would be beyond the scope of this book. msl.cs.uiuc.edu /planning/node819.html   (79 words)

Citebase - Path integrals and symmetry breaking for optimal control theory The transformation is similar to the transformation used to relate the classical Hamilton-Jacobi equation to the Schrödinger equation. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a linear equation. As a result of the linearity, the usual backward computation can be replaced by a forward diffusion process, that can be computed by stochastic integration or by the evaluation of a path integral. citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:physics/0505066   (469 words)

RESEARCH PUBLICATIONS FOR STAVROS A. BELBAS Iterative schemes for optimal control of certain integral equations, invited 1-hour lecture at the 1996 World Congress of Nonlinear Analysts; the corresponding paper, entitled “On the iterative solution of certain optimal control problems for Volterra integral equations”, is accepted for publication in the journal “Nonlinear Analysis - Theory, Methods, Applications.” Optimal control of certain Volterra integral equations with special constraints on the control, invited 30 minute lecture at the 1996 Volterra Centennial Symposium; extended summary has been published; the complete paper will be published in 1998, in a book, by the publishing company “Gordon and Breach”. Iterative schemes for the numerical solution of optimal control problems for Volterra equations, invited 1-hour lecture at the 1995 International Colloquium on Numerical Analysis; Abstract has been published. www.math.ua.edu /~sbelbas/publications.htm   (847 words)

bat.xml Stochastic differential equation, Hamilton-Jacobi-Bellman equation, Linear-Quadratic problem, Viscosity solutions, Applications to control theory. The paper studies the smoothness of solutions of the degenerate Hamilton-Jacobi-Bellman (HJB) equation associated with a linear-quadratic regulator control problem. We establish the existence of a classical solution of the degenerate HJB equation associated with this problem by the technique of viscosity solutions, and hence derive an optimal control from the optimality conditions in the HJB equation. www.emis.de /journals/LJM/vol17/bat.xml   (367 words)

Oxford Scholarship Online: Arbitrage Theory in Continuous Time We derive the Hamilton-Jacobi-Bellman equation as well as a verification theorem. Keywords: Hamilton-Jacobi-Bellman equation, optimal consumption, optimal control, optimal investment, stochastic differential equations This chapter gives a self-contained introduction to optimal control of stochastic differential equations. www.oxfordscholarship.com /oso/public/content/economicsfinance/0198775180/acprof-0198775180-chapter-14.html   (102 words)

Bohmian Mechanics In classical Hamilton-Jacobi theory we also have this equation for the velocity, but there the Hamilton-Jacobi function S can be entirely eliminated and the description in terms of S simplified and reduced to a finite-dimensional description, with basic variables the positions and the (unconstrained) momenta of all the particles, given by Hamilton's or Newton's equations. The theory is defined by the axioms governing the behavior of the basic observables -- Newton's equations for the positions or Hamilton's for positions and momenta. Since quantum theory itself, by virtue merely of the character of its predictions concerning EPR-Bohm correlations, is irreducibly nonlocal (see Section 2), one might expect considerable difficulty with the Lorentz invariance of orthodox quantum theory as well with Bohmian mechanics. plato.stanford.edu /entries/qm-bohm   (10692 words)

Bohmian Mechanics In classical Hamilton-Jacobi theory we also have this equation for the velocity, but there the Hamilton-Jacobi function S can be entirely eliminated and the description in terms of S simplified and reduced to a finite-dimensional description, with basic variables the positions and the (unconstrained) momenta of all the particles, given by Hamilton's or Newton's equations. Since quantum theory itself, by virtue merely of the character of its predictions concerning EPR-Bohm correlations, is irreducibly nonlocal (see Section 2), one might expect considerable difficulty with the Lorentz invariance of orthodox quantum theory as well with Bohmian mechanics. The quantum potential suggests, and indeed it has often been stated, that in order to transform Schrödinger's equation into a theory that can, in what are often called "realistic" terms, account for quantum phenomena, many of which are dramatically nonlocal, we must add to the theory a complicated quantum potential of a grossly nonlocal character. plato.stanford.edu /entries/qm-bohm   (10692 words)

Bohmian Mechanics In classical Hamilton-Jacobi theory we also have this equation for the velocity, but there the Hamilton-Jacobi function S can be entirely eliminated and the description in terms of S simplified and reduced to a finite-dimensional description, with basic variables the positions and the (unconstrained) momenta of all the particles, given by Hamilton's or Newton's equations. Since quantum theory itself, by virtue merely of the character of its predictions concerning EPR-Bohm correlations, is irreducibly nonlocal (see Section 2), one might expect considerable difficulty with the Lorentz invariance of orthodox quantum theory as well with Bohmian mechanics. The quantum potential suggests, and indeed it has often been stated, that in order to transform Schrödinger's equation into a theory that can, in what are often called "realistic" terms, account for quantum phenomena, many of which are dramatically nonlocal, we must add to the theory a complicated quantum potential of a grossly nonlocal character. plato.stanford.edu /entries/qm-bohm   (10692 words)

Session A1 - General Theory. Hamilton-Jacobi theory in momentum space is obtained by making a canonical transformation on Hamilton's equations using a generating function of the fourth type involving both the old and new momenta and time. When the classical limit of the Schroedinger equation in momentum space is taken (i.e., Planck's constant goes to zero) the Hamilton-Jacobi equation in momentum space is obtained. As an example, the Hamilton-Jacobi equation in momentum space is used to solve the harmonic oscillator. flux.aps.org /meetings/YR01/TSS01/abs/S100.html   (10692 words)

Sir William Rowan Hamilton --  Britannica Concise Encyclopedia - The online encyclopedia you can trust! Hamilton's approach was further refined by the German mathematician Carl Jacobi, and its significance became apparent in the development of celestial mechanics and quantum mechanics. Hamilton devoted the last 22 years of his life to the development of the theory of quaternions and related systems. For many years Hamilton sought to construct a theory of triplets, analogous to the couplets of complex numbers, that would be applicable to the study of three-dimensional geometry. www.britannica.com /ebc/article-9039042   (1723 words)

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