Work

Volume-surface systems with sub-quadratic intermediate sum on the surface: Global existence and boundedness

Year: 2025

Type: article

Abstract: The global existence and boundedness of solutions to volume-surface reaction diffusion systems with a mass control condition are investigated. Such systems arise typically in e.g. cell biology, ecology or fluid mechanics, when some concentrations or densities are inside a domain and some others are on its boundary. Comparing to previous works, the difficulty of systems under consideration here is that the nonlinearities on the surface can have sub-quadratic growth rates in all dimensions. To overcome this, we first use the Moser iteration to get some uniform bounds of the time integration of the solutions. Then, by combining these bounds with an $ L^p $-energy method and a duality argument, we obtain the global existence of solutions. Moreover, under mass dissipation conditions, the solution is shown to be bounded uniformly in time.

Source: Communications on Pure &amp Applied Analysis

DOI: 10.3934/cpaa.2025079

Authors: Juan Yang, Bao Quoc Tang

Institutions: University of Graz, Lanzhou University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Austrian Science Fund, China Scholarship Council

Awards: G2963376964, Quasi-steady state approximation for PDE, G4706507782