Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis

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Boundary spike‐layer solutions of the singular Keller–Segel system: existence and stability (2019, background): “[3, 4, 6, 13, 21, 23–26]), global well-posedness and/or asymptotic behavior of solutions (see [5, 8, 19, 20, 22, 28, 33, 37, 42, 43] in one dimensional bounded or unbounded space and [7, 9, 18, 22, 32, 35, 39, 41] in multidimensional spaces) and boundary layer solutions [10–12].”
Asymptotic stability of traveling waves of a chemotaxis model with singular sensitivity (2013, background): “1), the existence and stability of traveling wave solutions were given in [9,10].”
LARGE-TIME BEHAVIOR OF A PARABOLIC-PARABOLIC CHEMOTAXIS MODEL WITH LOGARITHMIC SENSITIVITY IN ONE DIMENSION (2012, methodology): “2) were recently studied in [37, 21, 22] for ε = 0 and in [23] for ε > 0, based on a Hopf-Cole type transformation”
Initial–boundary value problems for a system of hyperbolic balance laws arising from chemotaxis (2015, background): “[19–21]).”
Mathematics of traveling waves in chemotaxis --Review paper-- (2012, methodology): “22) means that (u−U, v− H)(x, t) = (φx, ψx)(x, t)→ 0 as t→∞, which is given in [47] for ε = 0 and in [49] for ε > 0, as follows:”
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.”