Global existence of entropy weak solutions and partial uniqueness are established for scalar balance laws with singular nonlocal sources, plus an Oleinik-type estimate and a local smoothness/wave-breaking criterion.
Stability and uniqueness for piecewise smooth solutions to a nonlocal scalar conservation law with applications to Burgers–Hilbert equation
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For frequency ω=3 and wave speed c≈1.1, the linearized operator around Burgers-Hilbert traveling waves has an eigenvalue with negative real part, shown via computer-assisted interval arithmetic.
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On scalar nonlinear balance laws with singular nonlocal sources
Global existence of entropy weak solutions and partial uniqueness are established for scalar balance laws with singular nonlocal sources, plus an Oleinik-type estimate and a local smoothness/wave-breaking criterion.
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Linear instability of a Burgers--Hilbert traveling wave
For frequency ω=3 and wave speed c≈1.1, the linearized operator around Burgers-Hilbert traveling waves has an eigenvalue with negative real part, shown via computer-assisted interval arithmetic.