Global Weak Solutions of a Hamiltonian Regularised Burgers Equation
نویسندگان
چکیده
A nondispersive, conservative regularisation of the inviscid Burgers equation is proposed and studied. Inspired by a related shallow water system recently introduced Clamond Dutykh, new provides family Galilean-invariant interpolants between Hunter–Saxton equation. It admits weakly singular regularised shocks cusped traveling-wave weak solutions. The breakdown local smooth solutions demonstrated, existence two types global solutions, conserving or dissipating an $$H^1$$ energy, established. Dissipative satisfy Oleinik inequality like entropy As scale parameter $$\ell $$ tends to 0 $$\infty , limits dissipative are shown respectively, forced unknown remaining term.
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ژورنال
عنوان ژورنال: Journal of Dynamics and Differential Equations
سال: 2022
ISSN: ['1040-7294', '1572-9222']
DOI: https://doi.org/10.1007/s10884-022-10171-0