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  • 1. Agram, N.
    et al.
    Haadem, S.
    Øksendal, B.
    Proske, F.
    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)
  • 2. Agram, Nacira
    et al.
    Bachouch, Achref
    Øksendal, Bernt
    Proske, Frank
    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)
  • 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.
    Bona, Jerry L.
    et al.
    Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago.
    Lenells, Jonatan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    The KdV Equation on the Half-Line: Time-Periodicity and Mass Transport2020In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 52, no 2, p. 1009-1039Article in journal (Refereed)
    Abstract [en]

    The work presented here emanates from questions arising from experimental observations of the propagation of surface water waves. The experiments in question featured a periodically moving wavemaker located at one end of a flume that generated unidirectional waves of relatively small amplitude and long wavelength when compared with the undisturbed depth. It was observed that the wave profile at any point down the channel very quickly became periodic in time with the same period as that of the wavemaker. One of the questions dealt with here is whether or not such a property holds for model equations for such waves. In the present discussion, this is examined in the context of the Korteweg-de Vries equation using the recently developed version of the inverse scattering theory for boundary-value problems put forward by Fokas and his collaborators. It turns out that solutions of the Korteweg-de Vries equation generated by periodic forcing at the boundary do exhibit asymptotic temporal periodicity at any fixed point down the channel. However, a more subtle issue to do with conservation of mass fails to hold at the second order in a small parameter, which is the typical wave amplitude divided by the undisturbed depth.

  • 6.
    Di Fratta, Giovanni
    et al.
    TU Wien, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria..
    Muratov, Cyrill B.
    New Jersey Inst Technol, Dept Math Sci, Newark, NJ 07102 USA..
    Rybakov, Filipp N.
    KTH, School of Engineering Sciences (SCI), Physics.
    Slastikov, Valeriy V.
    Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England..
    Variational principles of micromagnetics revisited2020In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 52, no 4, p. 3580-3599Article in journal (Refereed)
    Abstract [en]

    We revisit the basic variational formulation of the minimization problem associated with the micromagnetic energy, with an emphasis on the treatment of the stray field contribution to the energy, which is intrinsically nonlocal. Under minimal assumptions, we establish three distinct variational principles for the stray field energy: a minimax principle involving magnetic scalar potential and two minimization principles involving magnetic vector potential. We then apply our formulations to the dimension reduction problem for thin ferromagnetic shells of arbitrary shapes.

  • 7. 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].

  • 8. Goodman, Jonathan
    et al.
    Szepessy, Anders
    KTH, Superseded Departments (pre-2005), 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.

  • 9.
    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.

  • 10.
    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.

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