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  • 1.
    Agram, Nacira
    et al.
    University of Oslo, Norway;University of Mohamed Khider, Algeria.
    Bachouch, Achref
    University of Oslo, Norway.
    Oksendal, Bernt
    University of Oslo, Norway.
    Proske, Frank
    University of Oslo, Norway.
    Singular Control Optimal Stopping of Memory Mean-Field Processes2019In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 51, no 1, p. 450-468Article in journal (Refereed)
    Abstract [en]

    The purpose of this paper is to study the following topics and the relation between them: (i) Optimal singular control of mean-field stochastic differential equations with memory; (ii) reflected advanced mean-field backward stochastic differential equations; and (iii) optimal stopping of mean-field stochastic differential equations. More specifically, we do the following: (1) We prove the existence and uniqueness of the solutions of some reflected advanced memory backward stochastic differential equations; (2) we give sufficient and necessary conditions for an optimal singular control of a memory mean-field stochastic differential equation (MMSDE) with partial information; and (3) we deduce a relation between the optimal singular control of an MMSDE and the optimal stopping of such processes.

  • 2.
    Agram, Nacira
    et al.
    University Med Khider, Algeria.
    Haadem, Sven
    Linnaeus University, Faculty of Technology, Department of Mathematics. University of Oslo, Norway.
    Oksendal, Bernt
    University Med Khider, Algeria.
    Proske, Frank
    University of Oslo, Norway.
    A maximum principle for infinite horizon delay equations2013In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 45, no 4, p. 2499-2522Article in journal (Refereed)
    Abstract [en]

    We prove a maximum principle of optimal control of stochastic delay equations on infinite horizon. We establish first and second sufficient stochastic maximum principles as well as necessary conditions for that problem. We illustrate our results with an application to the optimal consumption rate from an economic quantity.

  • 3.
    Aleksanyan, Hayk
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). University of Edinburgh, United Kingdom.
    Slow convergence in periodic homogenization problems for divergence-type elliptic operators2016In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 48, no 5, p. 3345-3382Article in journal (Refereed)
    Abstract [en]

    We introduce a new constructive method for establishing lower bounds on convergence rates of periodic homogenization problems associated with divergence-type elliptic operators. The construction is applied in two settings. First, we show that solutions to boundary layer problems for divergence-type elliptic equations set in halfspaces and with in finitely smooth data may converge to their corresponding boundary layer tails as slowly as one wishes depending on the position of the hyperplane. Second, we construct a Dirichlet problem for divergence-type elliptic operators set in a bounded domain, and with all data being C-infinity-smooth, for which the boundary value homogenization holds with arbitrarily slow speed.

  • 4. Allen, Mark
    et al.
    Lindgren, Erik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Petrosyan, Arshak
    THE TWO-PHASE FRACTIONAL OBSTACLE PROBLEM2015In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 47, no 3, p. 1879-1905Article in journal (Refereed)
    Abstract [en]

    We study minimizers of the functional integral(+)(B1) vertical bar del u vertical bar(2)x(n)(a) dx + 2 integral(')(B1)(lambda + u(+) + lambda-u(-)) dx' for a is an element of (- 1, 1). The problem arises in connection with heat flow with control on the boundary. It can also be seen as a nonlocal analogue of the, by now well studied, two-phase obstacle problem. Moreover, when u does not change signs this is equivalent to the fractional obstacle problem. Our main results are the optimal regularity of the minimizer and the separation of the two free boundaries Gamma(+) = partial derivative'{u(center dot, 0) > 0} and Gamma(-) = partial derivative' {u(center dot, 0) < 0} when a >= 0.

  • 5. Berninger, H.
    et al.
    Frénod, E.
    Gander, M.
    Liebendörfer, M.
    Michaud, Jérôme
    Université de Genèeve, Genève, Switzerland.
    Derivation of the Isotropic Diffusion Source Approximation (IDSA) for Supernova Neutrino Transport by Asymptotic Expansions2013In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 45, no 6, p. 3229-3265Article in journal (Refereed)
  • 6.
    Chiadò Piat, V.
    et al.
    Politecnico di Torino, Torino, Italy.
    Pankratova, Iryna
    Narvik University College, Narvik, Norway.
    Piatnitski, A.
    Narvik University College, Narvik, Norway; P.N. Lebedev Physical Institute RAS, Moscow, Russian Federation.
    Localization effect for a spectral problem in a perforated domain with Fourier boundary conditions2013In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 45, no 3, p. 1302-1327Article in journal (Refereed)
    Abstract [en]

    This paper is aimed at homogenization of an elliptic spectral problem stated in a perforated domain, Fourier boundary conditions being imposed on the boundary of perforation. The presence of a locally periodic coefficient in the boundary operator gives rise to the effect of localization of the eigenfunctions. Moreover, the limit behavior of the lower part of the spectrum can be described in terms of an auxiliary harmonic oscillator operator. We describe the asymptotics of the eigenpairs and derive estimates for the rate of convergence. 

  • 7.
    Evers, J. H. M.
    et al.
    Simon Fraser University, Canada; Dalhousie University, Canada; Eindhoven University of Technology, Netherlands.
    Hille, S. C.
    Leiden University, Netherlands.
    Muntean, Adrian
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities2016In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 48, no 3, p. 1929-1953Article in journal (Refereed)
    Abstract [en]

    In this paper we prove well-posedness for a measure-valued continuity equation with solution-dependent velocity and flux boundary conditions, posed on a bounded one-dimensional domain. We generalize the results of an earlier paper [J. Differential Equations, 259 (2015), pp. 10681097] to settings where the dynamics are driven by interactions. In a forward-Euler-like approach, we construct a time-discretized version of the original problem and employ those results as a building block within each subinterval. A limit solution is obtained as the mesh size of the time discretization goes to zero. Moreover, the limit is independent of the specific way of partitioning the time interval [0, T]. This paper is partially based on results presented in Chapter 5 of [Evolution Equations for Systems Governed by Social Interactions, Ph.D. thesis, Eindhoven University of Technology, 2015], while a number of issues that were still open there are now resolved.

  • 8. Fainsilber, L.
    et al.
    Kurlberg, Pär
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Wennberg, B.
    Lattice points on circles and discrete velocity models for the Boltzmann equation2006In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 37, no 6, p. 1903-1922Article in journal (Refereed)
    Abstract [en]

    The construction of discrete velocity models or numerical methods for the Boltzmann equation, may lead to the necessity of computing the collision operator as a sum over lattice points. The collision operator involves an integral over a sphere, which corresponds to the conservation of energy and momentum. In dimension two there are difficulties even in proving the convergence of such an approximation since many circles contain very few lattice points, and some circles contain many badly distributed lattice points. However, by showing that lattice points on most circles are equidistributed we find that the collision operator can indeed be approximated as a sum over lattice points in the two-dimensional case. The proof uses a weak form of the Halberstam-Richert inequality for multiplicative functions (a proof is given in the paper), and estimates for the angular distribution of Gaussian primes. For higher dimensions, this result has already been obtained by Palczewski, Schneider, and Bobylev [SIAM J. Numer. Anal., 34 (1997), pp. 1865-1883].

  • 9. Goodman, Jonathan
    et al.
    Szepessy, Anders
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Zumbrun, Kevin
    A remark on the stability of viscous shock-waves1994In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 25, no 6, p. 1463-1467Article in journal (Refereed)
    Abstract [en]

    Recently, Szepessy and Xin gave a new proof of stability of viscous shock waves. A curious aspect of their argument is a possible disturbance of zero mass, but log(t)t-1/2 amplitude in the vicinity of the shock wave. This would represent a previously unobserved phenomenon. However, only an upper bound is established in their proof. Here, we present an example of a system for which this phenomenon can be verified by explicit calculation. The disturbance near the shock is shown to be precisely of order t-1/2 in amplitude.

  • 10.
    Hynd, Ryan
    et al.
    Univ Penn, Dept Math, Philadelphia, PA 19104 USA.
    Lindgren, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden.
    LIPSCHITZ REGULARITY FOR A HOMOGENEOUS DOUBLY NONLINEAR PDE2019In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 51, no 4, p. 3606-3624Article in journal (Refereed)
    Abstract [en]

    We study the doubly nonlinear PDE vertical bar partial derivative u vertical bar(p-2)partial derivative(t)u - div(vertical bar del u vertical bar(p-2)del u) = 0. This equation arises in the study of extremals of Poincare inequalities in Sobolev spaces. We prove spatial Lipschitz continuity and Holder continuity in time of order (p - 1)/p for viscosity solutions. As an application of our estimates, we obtain pointwise control of the large time behavior of solutions.

  • 11.
    Ioannidis, Andreas
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Kristensson, Gerhard
    Stratis, Ioannis G.
    On the Well-Posedness of the Maxwell System for Linear Bianisotropic Media2012In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 44, no 4, p. 2459-2473Article in journal (Refereed)
    Abstract [en]

    The time-dependent Maxwell system is supplemented with the constitutive relations of linear bianisotropic media and is treated as a neutral integro-differential equation in a Hilbert space. By using the theory of abstract Volterra equations and strongly continuous semigroups we obtain general well-posedness results for the corresponding mathematical problem.

  • 12.
    Kamotski, I. V.
    et al.
    UCL, London, England .
    Maz´ya, Vladimir
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    On the Linear Water Wave Problem in the Presence of a Critically Submerged Body2012In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 44, no 6, p. 4222-4249Article in journal (Refereed)
    Abstract [en]

    We study the two-dimensional problem of propagation of linear water waves in deep water in the presence of a critically submerged body (i.e., the body touching the water surface). Assuming uniqueness of the solution in the energy space, we prove the existence of a solution which satisfies the radiation conditions at infinity as well as at the cusp point where the body touches the water surface. This solution is obtained by the limiting absorption procedure. Next we introduce a relevant scattering matrix and analyze its properties. Under a geometric condition introduced by V. Mazya in 1978, we prove an important property of the scattering matrix, which may be interpreted as the absence of total internal reflection. This property also allows us to obtain uniqueness and existence of a solution in some function spaces (e.g., H-loc(2) boolean AND L-infinity) without use of the radiation conditions and the limiting absorption principle, provided a spectral parameter in the boundary conditions on the surface of the water is large enough. The fact that the existence and uniqueness result does not rely on either the radiation conditions or the limiting absorption principle is the first result of this type known to us in the theory of linear wave problems in unbounded domains.

  • 13.
    Kreiss, Heinz-Otto
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Parter, Seymour V.
    Remarks on singular perturbations with turning points1974In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 5, p. 230-251Article in journal (Refereed)
  • 14.
    Lenells, Jonatan
    University of California, United States .
    The hunter-saxton equation: A geometric approach2008In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 40, no 1, p. 266-277Article in journal (Refereed)
    Abstract [en]

    We provide a rigorous foundation for the geometric interpretation of the Hunter-Saxton equation as the equation describing the geodesic flow of the H 1 right-invariant metric on the quotient space Rot(double-struck S)\D k(double-struck S) of the infinite-dimensional Banach manifold D k(double-struck S) of orientationpreserving H k- diffeomorphisms of the unit circle double-struck S modulo the subgroup of rotations Rot(double-struck S). Once the underlying Riemannian structure has been established, the method of characteristics is used to derive explicit formulas for the geodesies corresponding to the H 1 right-invariant metric, yielding, in particular, new explicit expressions for the spatially periodic solutions of the initial-value problem for the Hunter-Saxton equation.

  • 15.
    Lenells, Jonatan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    The nonlinear steepest descent method: Asymptotics for initial-boundary value problems2016In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 48, no 3, p. 2076-2118Article in journal (Refereed)
    Abstract [en]

    We consider the rigorous derivation of asymptotic formulas for initial-boundary value problems using the nonlinear steepest descent method. We give detailed derivations of the asymptotics in the similarity and self-similar sectors for the modified Korteweg-de Vries equation in the quarter-plane. Precise and uniform error estimates are presented in detail.

  • 16.
    Löbus, Jörg-Uwe
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    Boundedness of the Stationary Solution to the Boltzmann Equation with Spatial Smearing, Diffusive Boundary Conditions, and Lions’ Collision Kernel2018In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 50, no 6, p. 5761-5782Article in journal (Refereed)
    Abstract [en]

    We investigate the Boltzmann equation with spatial smearing, diffusive boundary conditions, and Lions’ collision kernel. Both the physical as well as the velocity space, are assumed to be bounded. Existence and uniqueness of a stationary solution, which is a probability density, has been demonstrated in [S. Caprino, M. Pulvirenti, and W. Wagner, SIAM J. Math. Anal., 29 (1998), pp. 913–934] under a certain smallness assumption on the collision term. We prove that whenever there is a stationary solution then it is a.e. positively bounded from below and above.

1 - 16 of 16
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