Well-posedness of a dissolution-growth problem on an unbounded domain

Abstract

We consider a spherical grain which may be growing by accretion or dissolving in a dilute solution of the same substance where one also has reaction and diffusion. The resulting free boundary problem is shown to be well-posed and additional regularity is obtained.

Keywords:

• Stefan problem with surface tension
• unbounded domain
• free boundary problem
• radial geometry
• system
• parabolic
• partial differential equation
• reaction/diffusion
• well-posedness
• regularity