Quasilinear Degenerate Evolution Systems Modelling Biofilm Growth: Well‐Posedness and Qualitative Properties

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Analysis reveals well-posedness and uniqueness of solutions in biofilm modeling systems, indicating key mathematical properties.

Well-posedness established for Dirichlet and mixed boundary conditions, showing strong theoretical foundations for biofilm models.
Existence and uniqueness of weak solutions were proven under general assumptions, boosting confidence in the model's applicability.
The method employed involved regularized systems and fixed point arguments, enhancing the mathematical rigor of the analysis.
Findings indicate that solutions can exhibit global spatial regularity under certain growth conditions of the diffusion coefficient.

Mitra et al. (2025) studied this question.

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