Long-time asymptotics for coagulation equations with injection that do not have stationary solutions

Article Mathematics, Applied

Coagulation-Fragmentation Equations with Multiplicative Coagulation Kernel and Constant Fragmentation Kernel

Hung V. Tran et al.

Summary: This study focuses on a critical case of coagulation-fragmentation equations with a multiplicative coagulation kernel and constant fragmentation kernel. The method used involves studying viscosity solutions to a new singular Hamilton-Jacobi equation, which is derived from applying the Bernstein transform to the original coagulation-fragmentation equation. Results of this study include well-posedness, regularity, and long-time behaviors of viscosity solutions to the Hamilton-Jacobi equation in certain regimes, which have implications for well-posedness and long-time behaviors of mass-conserving solutions to the coagulation-fragmentation equation.

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS (2022)

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Article Mathematics, Applied

Stationary Non-equilibrium Solutions for Coagulation Systems

Marina A. Ferreira et al.

Summary: The study focuses on coagulation equations under non-equilibrium conditions induced by a source term for small cluster sizes. It is found that the two weight function parameters determine the existence of stationary solutions, with diffusive kernels allowing for their existence while free molecular kernels do not. Lower and upper estimates for solutions for large cluster sizes are obtained, and it is proved that the behavior of discrete model solutions asymptotically resembles that of continuous model solutions.

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2021)

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Article Chemistry, Physical