Some Qualitative Properties of Solutions to a Pseudoparabolic Equation Modeling Solvent Uptake in Polymeric Solids
Wolf‐Patrick Düll · Communications in Partial Differential Equations · 2006
In this paper we investigate the following pseudoparabolic differential equation: This equation models solvent uptake in polymeric solids. In this context ϕ stands for the concentration of the solvent, D for the diffusion coefficient, and η for the viscosity of the polymer. We characterize the long-time behavior of solutions, provided that D(ϕ) and (η(ϕ))−1 are bounded away from zero. For constitutive laws of the form D(ϕ) = ϕ m with m > 0 and η(ϕ) = 1 we prove short-time existence of solutions with constant, compact support.