Mathematical Biosciences and Engineering (MBE)

Structured populations with diffusion and Feller conditions
Pages: 261 - 279, Issue 2, April 2016

doi:10.3934/mbe.2015002      Abstract        References        Full text (1933.5K)           Related Articles

Agnieszka Bartłomiejczyk - Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland (email)
Henryk Leszczyński - Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland (email)

1 D. E. Apushkinskaya and N. I. Nazarov, A survey of results on nonlinear Wentzell problems, Appl. Math., 45 (2000), 69-80.       
2 J. Banasiak and M. Lachowicz, Methods of Small Parameter in Mathematical Biology, Birkhauser, 2014.       
3 A. Bartłomiejczyk and H. Leszczyński, Method of lines for physiologically structured models with diffusion, Appl. Numer. Math., 94 (2015), 140-148.       
4 A. Bartłomiejczyk and H. Leszczyński, Comparison principles for parabolic differential-functional initial-value problems, Nonlinear. Anal., 57 (2004), 63-84.       
5 A. Bobrowski and K. Morawska, From a PDE model to an ODE model of dynamics of synaptic depression, Disc. Cont. Dyn. Sys. Series B, 17 (2012), 2313-2327.       
6 A. Calsina and J. Z. Farkas, Steady states in a structured epidemic model with Wentzell boundary condition, J. Evol. Equat., 12 (2012), 495-512.       
7 J. M. Cushing, An Introduction to Structured Population Dynamics, SIAM, Philadelphia, 1998.       
8 K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer, New York, 2000.       
9 J. Z. Farkas and T. Hagen, Stability and regularity results for a size-structured population model, J. Math. Anal. App., 328 (2007), 119-136.       
10 J. Z. Farkas and P. Hinow, Physiologically structured populations with diffusion and dynamic boundary conditions, Math. Biosci. Eng., 8 (2011), 503-513.       
11 W. Feller, Diffusion processes in one dimension, Trans. Amer. Math. Soc., 77 (1954), 1-31.       
12 A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J. 1964.       
13 M. E. Gurtin and R. C. MacCamy, Diffusion models for age-structured populations, Math. Biosc., 54 (1981), 49-59.       
14 K. P. Hadeler, Structured populations with diffusion in state space, Math. Biosci. Eng., 7 (2010), 37-49.       
15 N. Kato, A general model of size-dependent population dynamics with nonlinear growth rate, J. Math. Anal. Appl., 297 (2004), 234-256.       
16 T. A. Kwembe and Z. Zhang, A semilinear equation with generalized Wentzell boundary condition, Non. Anal., 73 (2010), 3162-3170.       
17 O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Uraltseva, Linear and Quasi-linear Equations of Parabolic Type, (in Russian), Nauka, Moscow, 1967; (Translation of Mathematical Monographs, Vol. 23 Am. Math. Soc., Providence, R.I., 1968).       
18 P. Magal and S. Ruan, Structured Population Models in Biology and Epidemiology, Lecture Notes in Mathematics, Vol.1936, Springer-Verlag, Berlin, Heidelberg, 2008.       
19 J. A. J. Metz and O. Diekmann, The Dynamics of Physiologically Structured Populations, Lect. Notes in Biomath. Vol. 68, Springer, Berlin, 1986.       
20 B. Perthame, Transport Equations in Biology, Frontiers in Mathematics series, Birkhäuser, Boston, 2007.       
21 S. L. Tucker and S. O. Zimmermann, A nonlinear model of population dynamics containing an arbitrary number of continuous structure variables, SIAM J. Appl. Math., 48 (1988), 549-591.       
22 R. Waldstatter, K. P. Hadeler and G. Greiner, A Lotka-McKendrick model for a population structured by the level of parasitic infection, SIAM J. Math. Anal., 19 (1988), 1108-1118.       
23 W. Walter, Ordinary Differential Equations, Springer-Verlag, Berlin, Heidelberg, 1998.       
24 A. D. Wentzell, On boundary conditions for multi-dimensional diffusion processes, Theory Probab. Appl., 4 (1959), 164-177.       

Go to top