Exact solutions of a mathematical model for fluid transport in peritoneal dialysis

Ukrainian Mathematical Journal

Volumn 57, Issue 8, 2005, Pages 1316-1324

  Cherniha, R ^a   Waniewski, J ^b  

^a INSTITUTE OF MATHEMATICS   (Ukraine)

^b INSTITUTE OF BIOCYBERNETICS AND BIOMEDICAL ENGINEERING   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 30344439836     PISSN: 00415995     EISSN: 15739376     Source Type: Journal    
DOI: 10.1007/s11253-005-0263-y     Document Type: Article

References (10)

1. R. Gokal and K. D. Nolph (editors), The Textbook of Peritoneal Dialysis, Kluwer, Dordrecht (1994).
2. M. F. Flessner, "Transport of protein in the abdominal wall during intraperitoneal therapy. I. Theoretical approach," Amer. J. Physiol. Gastrointest. Liver Physiol., 281(2), 424-437 (2001).
3. J. Waniewski, "Physiological interpretation of solute transport parameters for peritoneal dialysis," J. Theor. Med., 3, 177-190 (2001).
4. L. V. Ovsyannikov, The Group Analysis of Differential Equations, Nauka, Moscow (1978).
5. P. Olver, Applications of Lie Groups to Differential Equations, Springer, Berlin (1986).
6. R. Cherniha and V. Dutka, "Exact and numerical solutions of the generalized Fisher equation," Rept. Math. Phys., 47, 393-411 (2001).
7. W. Fushchych and R. Cherniha, "The Galilean relativistic principle and nonlinear partial differential equations," J. Phys. A: Math. Gen., 18, 3491-3503 (1985).
8. R. M. Cherniha, "Nonlinear Galilei-invariant PDEs with infinite-dimensional Lie symmetry," J. Math. Anal. Appl., 253, 126-141 (2001).
9. R. M. Cherniha, "New non-Lie ans̈atze and exact solutions of nonlinear reaction-diffusion-convection equations," J. Phys. A: Math. Gen., 31, 8179-8198 (1998).
10. J. R. King, "Mathematical analysis of a model for substitutional diffusion," Proc. Roy. Soc. London A, 430, 377-404 (1990).