@article{53344,
  abstract     = {{<jats:p> A no-flux initial-boundary value problem for the cross-diffusion system [Formula: see text] is considered in smoothly bounded domains [Formula: see text] with [Formula: see text]. It is shown that whenever [Formula: see text] is positive on [Formula: see text] and such that [Formula: see text] for some [Formula: see text], for all suitably regular positive initial data a global very weak solution, particularly preserving mass in its first component, can be constructed. This extends previous results which either concentrate on non-degenerate analogs, or are restricted to the special case [Formula: see text]. </jats:p><jats:p> To appropriately cope with the considerably stronger cross-degeneracies thus allowed through [Formula: see text] when [Formula: see text] is large, in its core part the analysis relies on the use of the Moser–Trudinger inequality in controlling the respective diffusion rates [Formula: see text] from below. </jats:p>}},
  author       = {{Winkler, Michael}},
  issn         = {{1664-3607}},
  journal      = {{Bulletin of Mathematical Sciences}},
  keywords     = {{General Mathematics}},
  number       = {{02}},
  publisher    = {{World Scientific Pub Co Pte Ltd}},
  title        = {{{Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model}}},
  doi          = {{10.1142/s1664360722500126}},
  volume       = {{13}},
  year         = {{2022}},
}

@article{63284,
  abstract     = {{<jats:p> A no-flux initial-boundary value problem for the cross-diffusion system [Formula: see text] is considered in smoothly bounded domains [Formula: see text] with [Formula: see text]. It is shown that whenever [Formula: see text] is positive on [Formula: see text] and such that [Formula: see text] for some [Formula: see text], for all suitably regular positive initial data a global very weak solution, particularly preserving mass in its first component, can be constructed. This extends previous results which either concentrate on non-degenerate analogs, or are restricted to the special case [Formula: see text]. </jats:p><jats:p> To appropriately cope with the considerably stronger cross-degeneracies thus allowed through [Formula: see text] when [Formula: see text] is large, in its core part the analysis relies on the use of the Moser–Trudinger inequality in controlling the respective diffusion rates [Formula: see text] from below. </jats:p>}},
  author       = {{Winkler, Michael}},
  issn         = {{1664-3607}},
  journal      = {{Bulletin of Mathematical Sciences}},
  number       = {{02}},
  publisher    = {{World Scientific Pub Co Pte Ltd}},
  title        = {{{Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model}}},
  doi          = {{10.1142/s1664360722500126}},
  volume       = {{13}},
  year         = {{2022}},
}