| 1. |
- Andreasson, Håkan, 1966, et al.
(författare)
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Static solutions to the Einstein-Vlasov system with a nonvanishing cosmological constant
- 2015
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Ingår i: SIAM Journal on Mathematical Analysis. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1410 .- 1095-7111 .- 1095-7154. ; 47:4, s. 2657-2688
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Tidskriftsartikel (refereegranskat)abstract
- We construct spherically symmetric static solutions to the Einstein-Vlasov system with nonvanishing cosmological constant Λ. The results are divided as follows. For small Λ > 0 we show the existence of globally regular solutions which coincide with the Schwarzschild-deSitter solution in the exterior of the matter regions. For Λ < 0 we show via an energy estimate the existence of globally regular solutions which coincide with the Schwarzschild-anti-deSitter solution in the exterior vacuum region. We also construct solutions with a Schwarzschild singularity at the center regardless of the sign of Λ. For all solutions considered, the energy density and the pressure components have bounded support. Finally, we point out a straightforward method for obtaining a large class of global, nonvacuum spacetimes with topologies ℝ × S3 and ℝ × S2 × ℝ which arise from our solutions as a result of using the periodicity of the Schwarzschild-deSitter solution. A subclass of these solutions contains black holes of different masses.
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| 2. |
- Agram, Nacira, 1987-, et al.
(författare)
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A maximum principle for infinite horizon delay equations
- 2013
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Ingår i: SIAM Journal on Mathematical Analysis. - : Society for Industrial and Applied Mathematics. - 0036-1410 .- 1095-7154. ; 45:4, s. 2499-2522
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 3. |
- Agram, Nacira, 1987-, et al.
(författare)
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Singular Control Optimal Stopping of Memory Mean-Field Processes
- 2019
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Ingår i: SIAM Journal on Mathematical Analysis. - : Society for Industrial and Applied Mathematics. - 0036-1410 .- 1095-7154. ; 51:1, s. 450-468
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 4. |
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| 5. |
- Aleksanyan, Hayk
(författare)
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Slow convergence in periodic homogenization problems for divergence-type elliptic operators
- 2016
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Ingår i: SIAM Journal on Mathematical Analysis. - : Society for Industrial and Applied Mathematics. - 0036-1410 .- 1095-7154. ; 48:5, s. 3345-3382
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 6. |
- Allen, Mark, et al.
(författare)
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THE TWO-PHASE FRACTIONAL OBSTACLE PROBLEM
- 2015
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Ingår i: SIAM Journal on Mathematical Analysis. - : Society for Industrial and Applied Mathematics. - 0036-1410 .- 1095-7154. ; 47:3, s. 1879-1905
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 7. |
- Andreasson, Håkan, 1966, et al.
(författare)
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STATIC SOLUTIONS TO THE SPHERICALLY SYMMETRIC EINSTEIN-VLASOV SYSTEM: A PARTICLE NUMBER-CASIMIR APPROACH
- 2023
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Ingår i: SIAM Journal on Mathematical Analysis. - 1095-7154 .- 0036-1410. ; 55:5, s. 4843-4879
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Tidskriftsartikel (refereegranskat)abstract
- The existence of nontrivial static spherically symmetric solutions to the Einstein- Vlasov system is well-known. However, it is an open problem whether or not static solutions arise as minimizers of a variational problem. Apart from being of interest in its own right, it is the connection to nonlinear stability that gives this topic its importance. This problem was considered in [G. Wolansky, Arch. Ration. Mech. Anal., 156 (2001), pp. 205-230], but as has been pointed out in [H. Andr\'easson and M. Kunze, Arch. Ration. Mech. Anal., 235 (2020), pp. 783-791], that paper contained serious flaws. In this work we construct static solutions by solving the Euler- Lagrange equation for the energy density ρ as a fixed point problem. The Euler-Lagrange equation originates from the particle number-Casimir functional introduced in Wolansky (2001). We then define a density function f on phase space which induces the energy density \rho and we show that it constitutes a static solution of the Einstein-Vlasov system. Hence we settle rigorously parts of what Wolansky (2001) attempted to prove.
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| 8. |
- Arkeryd, Leif, 1940, et al.
(författare)
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Well-posedness of the Cauchy problem for a space-dependent anyon Boltzmann equation
- 2015
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Ingår i: SIAM Journal on Mathematical Analysis. - 0036-1410 .- 1095-7154. ; 47:6, s. 4720-4742
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Tidskriftsartikel (refereegranskat)abstract
- A fully non-linear kinetic Boltzmann equation for anyons is studied in a periodic 1d setting with large initial data. Strong L1 solutions are obtained for the Cauchy problem. The main results concern global existence, uniqueness, conservation of mass, momentum and energy, and stability.
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| 9. |
- Ben-Artzi, J., et al.
(författare)
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Arbitrarily Large Solutions of the Vlasov-Poisson System
- 2018
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Ingår i: SIAM Journal on Mathematical Analysis. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1410 .- 1095-7154. ; 50:4, s. 4311-4326
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Tidskriftsartikel (refereegranskat)abstract
- We study smooth, global-in-time solutions of the Vlasov--Poisson system in the plasma physical case that possess arbitrarily large charge densities and electric fields. In particular, we construct two classes of solutions with this property. The first class consists of spherically symmetric solutions that initially possess arbitrarily small density and field values but attain arbitrarily large values of these quantities at some later time. Additionally, we construct a second class of spherically symmetric solutions that possess any desired mass and attain arbitrarily large density and field values at any later prescribed time.
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| 10. |
- Ben-Artzi, Jonathan, et al.
(författare)
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Arbitrarily Large Solutions of the Vlasov-Poisson System
- 2018
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Ingår i: SIAM Journal on Mathematical Analysis. - 1095-7154 .- 0036-1410. ; 50:4, s. 4311-4326
-
Tidskriftsartikel (refereegranskat)abstract
- We study smooth, global-in-time solutions of the Vlasov-Poisson system in the plasma physical case that possess arbitrarily large charge densities and electric fields. In particular, we construct two classes of solutions with this property. The first class consists of spherically symmetric solutions that initially possess arbitrarily small density and field values but attain arbitrarily large values of these quantities at some later time. Additionally, we construct a second class of spherically symmetric solutions that possess any desired mass and attain arbitrarily large density and field values at any later prescribed time.
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