Empirical measures from Kac's particle system converge to the Boltzmann equation solution for very soft potentials, proving propagation of chaos for all kernel classes.
A Parabolic Problem with a Fractional Time Derivative
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Existence of self-similar finite-mass solutions is proved for the time-fractional porous-medium equation in the optimal range m > (d-2)_+/d for all d ≥ 1, with compact support for m > 1 and heavy tails for m_c < m < 1.
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.
Stability with sharp exponent 2 holds for the L^p-Talenti inequality when f is the characteristic function of a subset of the unit ball.
citing papers explorer
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Propagation of chaos for the Boltzmann equation with very soft potentials
Empirical measures from Kac's particle system converge to the Boltzmann equation solution for very soft potentials, proving propagation of chaos for all kernel classes.
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Self-similar solutions to the time-fractional Porous-Medium Equation
Existence of self-similar finite-mass solutions is proved for the time-fractional porous-medium equation in the optimal range m > (d-2)_+/d for all d ≥ 1, with compact support for m > 1 and heavy tails for m_c < m < 1.
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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.
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Sharp quantitative Talenti's inequality in particular cases
Stability with sharp exponent 2 holds for the L^p-Talenti inequality when f is the characteristic function of a subset of the unit ball.