This paper proposes a numerical scheme for the (2 + 1)-dimensional nonlinear Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation (ZK-BBME). The ZK-BBME represents a long-wave model with large wavelength that explains...
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Support Vector Machine (SVM) has received much attention in machine learning due to its profound theoretical research and practical application results. Support Vector Regression (SVR) has become a powerful tool for s...
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We present a method leveraging extreme learning machine (ELM) type randomized neural networks (NNs) for learning the exact time integration algorithm for initial value problems. The exact time integration algorithm fo...
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We consider an antiferromagnet in one space dimension with easy-axis anisotropy in a perpendicular magnetic field. We study propagating domain wall solutions that can have a velocity up to a maximum vc. The width of t...
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This paper concerns an inverse boundary value problem for a semilinear wave equation on a globally hyperbolic Lorentzian manifold. We prove a Hölder stability result for recovering an unknown potential ☆q☆...
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This paper concerns an inverse boundary value problem for a semilinear wave equation on a globally hyperbolic Lorentzian manifold. We prove a Hölder stability result for recovering an unknown potential ☆q☆ of the nonlinear wave equation ☆□☆g☆u☆+☆q☆u☆m☆=☆0☆, ☆m☆≥☆4☆, from the Dirichlet-to-Neumann map. Our proof is based on the recent higher-order linearization method and use of Gaussian beams. We also extend earlier uniqueness results by removing the assumptions of convex boundary and that pairs of light-like geodesics can intersect only once. For this, we construct special light-like geodesics and other general constructions in Lorentzian geometry. We expect these constructions to be applicable in studies of related problems as well.
In many drylands around the globe, vegetation self-organizes into regular spatial patterns in response to aridity stress. We consider the regularly-spaced vegetation bands, on gentle hill-slopes, that survive low rain...
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In the radiative Vlasov-Maxwell equations, the Lorentz force is modified by the addition of radiation reaction forces. The radiation forces produce damping of particle energy but the forces are no longer divergence-fr...
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We construct axisymmetric solutions to the three-dimensional parabolic-elliptic Keller-Segel system that blows up in finite time. In particular, the singularity is of type II, which admits locally a leading order prof...
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We study the existence and zero viscous limit of smooth solutions to steady compressible Navier-Stokes equations near plane shear flow between two moving parallel walls. Under the assumption 0 0 = (µ(x2), 0), the...
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