2017/01/25 by Johannes Lankeit, Michael Winkler, Lankeit, Johannes +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #35D99 #35K55 #92C17 #Analysis of PDEs (math.AP) #Cancer Genomics and Diagnostics #FOS: Mathematics #Gene Regulatory Network Analysis #MRI in cancer diagnosis #Mathematical Biology Tumor Growth #Statistical Methods in Clinical Trials
paper · pdf · doi:10.48550/arxiv.1701.07391
openalex publication_date 2017/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The chemotaxis system \
left
\ut =
Delta u -
chi
nabla\n
cdot (
fracuv
nabla v), vt=
Delta v - v+u, \
right. is\nconsidered in a bounded domain \Ω\⊂ \ℝn with smooth\nboundary, where \χ>0. An apparently novel type of generalized solution\nframework is introduced within which an extension of previously known ranges\nfor the key parameter \χ with regard to global solvability is achieved. In\nparticular, it is shown that under the hypothesis that\
chi lt;
left
\n∞
qquad · amp;
mboxif n=2,
sqrt8
qquad · amp;
mboxif \nn=3,
fracnn-2
qquad · amp;
mboxif n
ge 4, \
right. for all\ninitial data satisfying suitable assumptions on regularity and positivity, an\nassociated no-flux initial-boundary value problem admits a globally defined\ngeneralized solution. This solution inter alia has the property that \u
in\nL1loc(
bar
Omega
times [0,
infty)). n