Long-time convergence of a nonlocal Burgers’ equation towards the local N-wave
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2023-11-04
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Institute of Physics
Resumen
We study the long-time behaviour of the unique weak solution of a nonlocal regularisation of the (inviscid) Burgers equation where the velocity is approximated by a one-sided convolution with an exponential kernel. The initial datum is assumed to be positive, bounded, and integrable. The asymptotic profile is given by the ‘N-wave’ entropy solution of the Burgers equation. The key ingredients of the proof are a suitable scaling argument and a nonlocal Oleinik-type estimate.
Palabras clave
35L65
Approximation of local conservation laws
Burgers equation
Entropy solutions
N-waves
Nonlocal conservation laws
Nonlocal flux
Source-type solutions
Approximation of local conservation laws
Burgers equation
Entropy solutions
N-waves
Nonlocal conservation laws
Nonlocal flux
Source-type solutions
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Materias
Cita
Coclite, G. M., De Nitti, N., Keimer, A., Pflug, L., & Zuazua, E. (2023). Long-time convergence of a nonlocal Burgers’ equation towards the local N-wave. Nonlinearity, 36(11), 5998-6019. https://doi.org/10.1088/1361-6544/ACF01D