Global existence of solutions to a coupled coagulation system

Abstract

We consider a model equations describing the coagulation process of a gas on a surface. The problem is modeled by two coupled equations. The first one is a nonlinear transport equation with bilinear coagulation operator while the second one is a nonlinear ordinary differential equation. The velocity and the boundary condition of the transport equation depend on the supersaturation function satisfying the nonlinear ode. We first prove global existence and uniqueness of solution to the nonlinear transport equation then, we consider the coupled problem and prove existence in the large of solutions to the full coagulation system.

Keywords:

• Nonlinear hyperbolic equations
• nonlinear ordinary differential equations
• compensated compactness
• coagulation operator

AMS:

• 35F25
• 35L60
• 34A34
• 34B15

^*MAB Université Bordeaux 1 351 cours de la Libération 33405 Talence cedex ([email protected])

^†CNRS-Université Paris Nord. Institut Galilée. Laga. Avenue J.B Clement. 93430- Villetaneuse ([email protected])

^*MAB Université Bordeaux 1 351 cours de la Libération 33405 Talence cedex ([email protected])

^*MAB Université Bordeaux 1 351 cours de la Libération 33405 Talence cedex ([email protected])

^†CNRS-Université Paris Nord. Institut Galilée. Laga. Avenue J.B Clement. 93430- Villetaneuse ([email protected])

^*MAB Université Bordeaux 1 351 cours de la Libération 33405 Talence cedex ([email protected])

Notes

^*MAB Université Bordeaux 1 351 cours de la Libération 33405 Talence cedex ([email protected])

^†CNRS-Université Paris Nord. Institut Galilée. Laga. Avenue J.B Clement. 93430- Villetaneuse ([email protected])

^*MAB Université Bordeaux 1 351 cours de la Libération 33405 Talence cedex ([email protected])