Results 11 to 20 of about 2,221 (63)
The nonlinear Schrödinger equation on the half-line with homogeneous Robin boundary conditions. [PDF]
Proc Lond Math Soc, 2023 Abstract We consider the nonlinear Schrödinger equation on the half‐line x⩾0$x \geqslant 0$ with a Robin boundary condition at x=0$x = 0$ and with initial data in the weighted Sobolev space H1,1(R+)$H^{1,1}(\mathbb {R}_+)$. We prove that there exists a global weak solution of this initial‐boundary value problem and provide a representation for the ...
Lee JM, Lenells J.
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Traveling Wave Solutions to the Free Boundary Incompressible Navier‐Stokes Equations
Communications on Pure and Applied Mathematics, Volume 76, Issue 10, Page 2474-2576, October 2023., 2023 Abstract In this paper we study a finite‐depth layer of viscous incompressible fluid in dimension n≥2, modeled by the Navier‐Stokes equations. The fluid is assumed to be bounded below by a flat rigid surface and above by a free, moving interface. A uniform gravitational field acts perpendicularly to the flat surface, and we consider the cases with and ...
Giovanni Leoni, Ian Tice
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On fractional semidiscrete Dirac operators of Lévy–Leblond type
Mathematische Nachrichten, Volume 296, Issue 7, Page 2758-2779, July 2023., 2023 Abstract In this paper, we introduce a wide class of space‐fractional and time‐fractional semidiscrete Dirac operators of Lévy–Leblond type on the semidiscrete space‐time lattice hZn×[0,∞)$h{\mathbb {Z}}^n\times [0,\infty )$ (h>0$h>0$), resembling to fractional semidiscrete counterparts of the so‐called parabolic Dirac operators.
Nelson Faustino
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Communications on Pure and Applied Mathematics, Volume 75, Issue 12, Page 2685-2801, December 2022., 2022 Abstract This manuscript constructs global in time solutions to master equations for potential mean field games. The study concerns a class of Lagrangians and initial data functions that are displacement convex, and so this property may be in dichotomy with the so‐called Lasry–Lions monotonicity, widely considered in the literature.
Wilfrid Gangbo, Alpár R. Mészáros
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Journal of the London Mathematical Society, Volume 106, Issue 2, Page 590-661, September 2022., 2022 Abstract Given a generic stable strongly parabolic SL(2,C)$\operatorname{SL}(2,\mathbb {C})$‐Higgs bundle (E,φ)$({\mathcal {E}}, \varphi )$, we describe the family of harmonic metrics ht$h_t$ for the ray of Higgs bundles (E,tφ)$({\mathcal {E}}, t \varphi )$ for t≫0$t\gg 0$ by perturbing from an explicitly constructed family of approximate solutions ...
Laura Fredrickson +3 more
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Self‐adjoint and Markovian extensions of infinite quantum graphs
Journal of the London Mathematical Society, Volume 105, Issue 2, Page 1262-1313, March 2022., 2022 Abstract We investigate the relationship between one of the classical notions of boundaries for infinite graphs, graph ends, and self‐adjoint extensions of the minimal Kirchhoff Laplacian on a metric graph. We introduce the notion of finite volume for ends of a metric graph and show that finite volume graph ends is the proper notion of a boundary for ...
Aleksey Kostenko +2 more
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Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021 The Black‐Scholes model is well known for determining the behavior of capital asset pricing models in the finance sector. The present article deals with the Black‐Scholes model via the Caputo fractional derivative and Atangana‐Baleanu fractional derivative operator in the Caputo sense, respectively.
Saima Rashid +4 more
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Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021 In this paper, we introduce the Yang transform homotopy perturbation method (YTHPM), which is a novel method. We provide formulae for the Yang transform of Caputo‐Fabrizio fractional order derivatives. We derive an algorithm for the solution of Caputo‐Fabrizio (CF) fractional order partial differential equation in series form and show its convergence ...
Shabir Ahmad +4 more
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Semistatic and sparse variance‐optimal hedging
Mathematical Finance, Volume 30, Issue 2, Page 403-425, April 2020., 2020 Abstract We consider the problem of hedging a contingent claim with a “semistatic” strategy composed of a dynamic position in one asset and static (buy‐and‐hold) positions in other assets. We give general representations of the optimal strategy and the hedging error under the criterion of variance optimality and provide tractable formulas using Fourier
Paolo Di Tella +2 more
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On eigenfunction expansion of solutions to the Hamilton equations
, 2013 We establish a spectral representation for solutions to linear Hamilton equations with positive definite energy in a Hilbert space. Our approach is a special version of M.
Komech, Alexander, Kopylova, Elena
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