# Difference between revisions of "Applied/ACMS/absS20"

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Title: Coagulation-Fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel | Title: Coagulation-Fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel | ||

Abstract: We study a critical case of Coagulation-Fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel. Our method is based on the study of viscosity solutions to a new singular Hamilton-Jacobi equation, which results from applying the Bernstein transform to the original Coagulation-Fragmentation equation. Our results include wellposedness, regularity and long-time behaviors of viscosity solutions to the Hamilton-Jacobi equation in certain regimes, which have implications to wellposedness and long-time behaviors of mass-conserving solutions to the Coagulation-Fragmentation equation. Joint work with Truong-Son Van (CMU). | Abstract: We study a critical case of Coagulation-Fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel. Our method is based on the study of viscosity solutions to a new singular Hamilton-Jacobi equation, which results from applying the Bernstein transform to the original Coagulation-Fragmentation equation. Our results include wellposedness, regularity and long-time behaviors of viscosity solutions to the Hamilton-Jacobi equation in certain regimes, which have implications to wellposedness and long-time behaviors of mass-conserving solutions to the Coagulation-Fragmentation equation. Joint work with Truong-Son Van (CMU). |

## Revision as of 09:10, 4 November 2019

# ACMS Abstracts: Spring 2020

### Hung Tran

Title: Coagulation-Fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel

Abstract: We study a critical case of Coagulation-Fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel. Our method is based on the study of viscosity solutions to a new singular Hamilton-Jacobi equation, which results from applying the Bernstein transform to the original Coagulation-Fragmentation equation. Our results include wellposedness, regularity and long-time behaviors of viscosity solutions to the Hamilton-Jacobi equation in certain regimes, which have implications to wellposedness and long-time behaviors of mass-conserving solutions to the Coagulation-Fragmentation equation. Joint work with Truong-Son Van (CMU).