RT Journal Article
ID 7185d4387ae9385d
A1 Wojciechowski, Keith J. 
A1 Chen, Jinhai 
A1 Schreyer-Bennethum, Lynn 
A1 Sandberg, Kristian 
T1 WELL-POSEDNESS AND NUMERICAL SOLUTION OF A NONLINEAR VOLTERRA PARTIAL INTEGRO-DIFFERENTIAL EQUATION MODELING A SWELLING POROUS MATERIAL
JF Journal of Porous Media
JO JPM
YR 2014
FD 2014-10-16
VO 17
IS 9
SP 763
OP 784
K1 Volterra partial integro-differential equations
K1 pseudospectral methods
K1 swelling porous materials
K1 well-posedness
K1 viscoelasticity
AB We mathematically analyze an initial-boundary value problem that involves a nonlinear Volterra partial integro-differential equation derived using hybrid mixture theory and used to model swelling porous materials where the application is an immersed, porous cylindrical material imbibing fluid through its exterior boundary. The model is written as an initial-boundary value problem and we establish well-posedness and numerically solve it using a novel approach to constructing pseudospectral differentiation matrices in a polar geometry. Numerical results are obtained and interpretations are provided for a small variety of diffusion and permeability coefficients and parameters to simulate the model's behavior and to demonstrate its viability as a model for swelling porous materials exhibiting viscoelastic behavior.
PB Begell House
LK https://www.dl.begellhouse.com/journals/49dcde6d4c0809db,69cb9f9c2a8eb0bd,7185d4387ae9385d.html