Well-posedness via fixed point, mass preservation, gradient-flow energy structure, decay estimates, and singular limit to a fully parabolic system are established for local-nonlocal parabolic-elliptic models with Neumann conditions.
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XekRung achieves state-of-the-art performance on cybersecurity benchmarks among same-scale models via tailored data synthesis and multi-stage training while retaining strong general capabilities.
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Parabolic--Elliptic Dynamics with Local--Nonlocal Coupled Operators
Well-posedness via fixed point, mass preservation, gradient-flow energy structure, decay estimates, and singular limit to a fully parabolic system are established for local-nonlocal parabolic-elliptic models with Neumann conditions.
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XekRung Technical Report
XekRung achieves state-of-the-art performance on cybersecurity benchmarks among same-scale models via tailored data synthesis and multi-stage training while retaining strong general capabilities.