<div class="csl-bib-body">
<div class="csl-entry">Helmer, C., & Jüngel, A. (2023). Existence analysis for a reaction-diffusion Cahn–Hilliard-type system with degenerate mobility and singular potential modeling biofilm growth. <i>Discrete and Continuous Dynamical Systems - Series A</i>, <i>43</i>(10), 3839–3861. https://doi.org/10.3934/dcds.2023069</div>
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dc.identifier.issn
1078-0947
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/190372
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dc.description.abstract
The global existence of bounded weak solutions to a diffusion system modeling biofilm growth is proven. The equations consist of a reaction-diffusion equation for the substrate concentration and a fourth-order Cahn–Hilliard-type equation for the volume fraction of the biomass, considered in a bounded domain with no-flux boundary conditions. The main difficulties are coming from the degenerate diffusivity and mobility, the singular potential arising from a logarithmic free energy, and the nonlinear reaction rates. These issues are overcome by a truncation technique and a Browder–Minty trick to identify the weak limits of the reaction terms. The qualitative behavior of the solutions is illustrated by numerical experiments in one space dimension, using a BDF2 (second-order backward Differentiation Formula) finite-volume scheme.
en
dc.language.iso
en
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dc.publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
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dc.relation.ispartof
Discrete and Continuous Dynamical Systems - Series A
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dc.subject
Biofilms
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dc.subject
Cahn–Hilliard equation
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dc.subject
degenerate mobility
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dc.subject
existence of solutions
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dc.subject
logarithmic free energy
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dc.subject
reaction-diffusion equation
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dc.subject
singular potential
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dc.title
Existence analysis for a reaction-diffusion Cahn–Hilliard-type system with degenerate mobility and singular potential modeling biofilm growth