NONLINEAR STABILITY OF LARGE AMPLITUDE VISCOUS SHOCK WAVES OF A GENERALIZED HYPERBOLIC–PARABOLIC SYSTEM ARISING IN CHEMOTAXIS

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The two-dimensional Keller–Segel system with singular sensitivity and signal absorption: Global large-data solutions and their relaxation properties (2016, background): “1) ([17], [26], [27]), and also to some closely related systems ([35], [30], [32]).”
Mathematics of traveling waves in chemotaxis --Review paper-- (2012, methodology): “The result for C0 6= 0 still largely remains open except for the case m = 1 which was solved in [83, 47, 48, 49] for ε ≥ 0 and in [9] for ε = 0 by different methods, which will be sketched below.”
Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis (2011, methodology): “ε = 0), and was later applied in [12,13] to study the nonlinear stability of traveling wave solutions.”
Initial–boundary value problems for a system of hyperbolic balance laws arising from chemotaxis (2015, background): “[19–21]).”
Well-posedness of a 3D parabolic–hyperbolic Keller–Segel system in the Sobolev space framework (2012, unknown): “[5, 7, 8, 10, 13, 14, 15, 16, 21, 22, 23, 25, 26, 27, 28, 30, 31, 34, 35, 36, 37] for more discussions in this direction.”