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Convergence rates towards the traveling waves for a model system of radiating gas with discontinuities
An agestructured twosex model in the space of radon measures: Well posedness
1.  University of Warsaw, ul. Banacha 2, 02097 Warsaw, Poland 
References:
[1] 
L. Ambrosio, N. Gigli and G. Savaré, "Gradient Flows in Metric Spaces and in the Space of Probability Measures," Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 2005. Google Scholar 
[2] 
J. A. Cañizo, J. A. Carrillo and S. Cuadrado, Measure solutions for some models in population dynamics, Acta Applicandae Mathematicae, (2012), 116. Google Scholar 
[3] 
J. A. Carrillo, R. M. Colombo, P. Gwiazda and A. Ulikowska, Structured populations, cell growth and measure valued balance laws, Journal of Differential Equations, 252 (2012), 32453277. Google Scholar 
[4] 
C. CastilloChávez and W. Huang, The logistic equation revisited, Math. Biosci., 128 (1995), 199316. Google Scholar 
[5] 
O. Diekmann and J.A.J. Metz, "The dynamics of Physiologically Structured populations," Lecture Notes in Biomathematics, 68, SpringerVerlag, Berlin, 1986. Google Scholar 
[6] 
K. Dietz and K. P. Hadeler, Epidemiological models for sexually transmitted diseases, J. Math. Biol., 26 (1988), 125. Google Scholar 
[7] 
L. C. Evans, "Weak Convergence Methods for Nonlinear Partial Differential Equations," CBMS Regional Conference Series in Mathematics, 74, published for the Conference Board of the Mathematical Sciences, Washington, DC, 1990. Google Scholar 
[8] 
L. C. Evans, "Partial Differential Equations," Graduate Studies in Mathematics, 19, American Mathematical Society, Providence, RI, 2010. Google Scholar 
[9] 
A. Fredrickson, A mathematical theory of age structure in sexual populations: random mating and monogamous models, Math. Biosci., 10 (1971), 117143. doi: 10.1016/00255564(71)90054X. Google Scholar 
[10] 
A. Fredrickson and P. Hsu, Populationchanging processes and the dynamics of sexual populations, Math. Biosci., 26 (1975), 5578. doi: 10.1016/00255564(75)900942. Google Scholar 
[11] 
G. Garnett, An introduction to mathematical models in sexually transmitted disease epidemiology, Sex Transm. Inf., 78 (2001), 712. Google Scholar 
[12] 
P. Gwiazda, G. Jamróz and A. MarciniakCzochra, Models of discrete and continuous cell differentiation in the framework of transport equation, SIAM J. Math. Anal., 44 (2012), 11031133. Google Scholar 
[13] 
P. Gwiazda, T. Lorenz and A. MarciniakCzochra, A nonlinear structured population model: Lipschitz continuity of measurevalued solutions with respect to model ingredients, Journal of Differential Equations, 248 (2010), 27032735. Google Scholar 
[14] 
P. Gwiazda and A. MarciniakCzochra, Structured population equations in metric spaces, J. Hyperbolic Differ. Equ., 7 2010, 733773. Google Scholar 
[15] 
K. Hadeler and K. Ngoma, Homogeneous models for sexually transmitted diseases, Rocky Mt. J. Math., 20 (1990), 967986. Google Scholar 
[16] 
K. P. Hadeler, Pair formation in agestructured populations, Acta Appl. Math., 14 (1989), 91102. Google Scholar 
[17] 
K. P. Hadeler, R. Waldstätter and A. WörzBusekros, Models for pair formation in bisexual populations, J. Math. Biol., 26 (1988), 635649. doi: 10.1007/BF00276145. Google Scholar 
[18] 
F. Hoppensteadt, "Mathematical Theories of Populations: Demographics, Genetics and Epidemics," Society for Industrial and Applied Mathematics, Philadelphia, PA, 1975. Google Scholar 
[19] 
M. Iannelli, M. Martcheva and F. A. Milner, "Genderstructured Population Modeling. Mathematical Methods, Numerics, and Simulations," Frontiers in Applied Mathematics, 31, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2005. Google Scholar 
[20] 
H. Inaba, "An Agestructured Twosex Model for Human Population Reproduction by First Marriage," volume 15 of Working paper series, Institute of Population Problems, Tokyo, 1993. Google Scholar 
[21] 
H. Inaba, Persistent age distributions for an agestructured twosex population model, Math. Population Studies, 7 (2000), 365398. Google Scholar 
[22] 
D. G. Kendall, Stochastic processes and population growth, J. Roy. Statist. Soc. Ser. B., 11 (1949), 230264. Google Scholar 
[23] 
M. Martcheva, Exponential growth in agestructured twosex populations, Math. Biosci., 157 (1999), 122. Google Scholar 
[24] 
M. Martcheva and F. A. Milner, A twosex agestructured population model: well posedness, Math. Population Stud., 7 (1999), 111129. Google Scholar 
[25] 
M. Martcheva and F. A. Milner, The mathematics of sex and marriage, revisited, Math. Population Stud., 9 (2001), 123141. Google Scholar 
[26] 
D. Maxin and F. Milner, The effect of nonreproductive groups on persistent sexually transmitted diseases, Math. Biosc. and Engin., 4 (2007), 505522. doi: 10.3934/mbe.2007.4.505. Google Scholar 
[27] 
F. Milner and K. Yang, The logistic, twosex, agestructured population model, J. Biol. Dyn., 3 (2009), 252270. Google Scholar 
[28] 
J. Prüss and W. Schappacher, Persistent agedistributions for a pairformation model, J. Math. Biol., 33 (1994), 1733. Google Scholar 
[29] 
G. F. Webb, "Structured Population Dynamics," Banach Center Publications, 63, Polish Acad. Sci., Warsaw, 2004. Google Scholar 
show all references
References:
[1] 
L. Ambrosio, N. Gigli and G. Savaré, "Gradient Flows in Metric Spaces and in the Space of Probability Measures," Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 2005. Google Scholar 
[2] 
J. A. Cañizo, J. A. Carrillo and S. Cuadrado, Measure solutions for some models in population dynamics, Acta Applicandae Mathematicae, (2012), 116. Google Scholar 
[3] 
J. A. Carrillo, R. M. Colombo, P. Gwiazda and A. Ulikowska, Structured populations, cell growth and measure valued balance laws, Journal of Differential Equations, 252 (2012), 32453277. Google Scholar 
[4] 
C. CastilloChávez and W. Huang, The logistic equation revisited, Math. Biosci., 128 (1995), 199316. Google Scholar 
[5] 
O. Diekmann and J.A.J. Metz, "The dynamics of Physiologically Structured populations," Lecture Notes in Biomathematics, 68, SpringerVerlag, Berlin, 1986. Google Scholar 
[6] 
K. Dietz and K. P. Hadeler, Epidemiological models for sexually transmitted diseases, J. Math. Biol., 26 (1988), 125. Google Scholar 
[7] 
L. C. Evans, "Weak Convergence Methods for Nonlinear Partial Differential Equations," CBMS Regional Conference Series in Mathematics, 74, published for the Conference Board of the Mathematical Sciences, Washington, DC, 1990. Google Scholar 
[8] 
L. C. Evans, "Partial Differential Equations," Graduate Studies in Mathematics, 19, American Mathematical Society, Providence, RI, 2010. Google Scholar 
[9] 
A. Fredrickson, A mathematical theory of age structure in sexual populations: random mating and monogamous models, Math. Biosci., 10 (1971), 117143. doi: 10.1016/00255564(71)90054X. Google Scholar 
[10] 
A. Fredrickson and P. Hsu, Populationchanging processes and the dynamics of sexual populations, Math. Biosci., 26 (1975), 5578. doi: 10.1016/00255564(75)900942. Google Scholar 
[11] 
G. Garnett, An introduction to mathematical models in sexually transmitted disease epidemiology, Sex Transm. Inf., 78 (2001), 712. Google Scholar 
[12] 
P. Gwiazda, G. Jamróz and A. MarciniakCzochra, Models of discrete and continuous cell differentiation in the framework of transport equation, SIAM J. Math. Anal., 44 (2012), 11031133. Google Scholar 
[13] 
P. Gwiazda, T. Lorenz and A. MarciniakCzochra, A nonlinear structured population model: Lipschitz continuity of measurevalued solutions with respect to model ingredients, Journal of Differential Equations, 248 (2010), 27032735. Google Scholar 
[14] 
P. Gwiazda and A. MarciniakCzochra, Structured population equations in metric spaces, J. Hyperbolic Differ. Equ., 7 2010, 733773. Google Scholar 
[15] 
K. Hadeler and K. Ngoma, Homogeneous models for sexually transmitted diseases, Rocky Mt. J. Math., 20 (1990), 967986. Google Scholar 
[16] 
K. P. Hadeler, Pair formation in agestructured populations, Acta Appl. Math., 14 (1989), 91102. Google Scholar 
[17] 
K. P. Hadeler, R. Waldstätter and A. WörzBusekros, Models for pair formation in bisexual populations, J. Math. Biol., 26 (1988), 635649. doi: 10.1007/BF00276145. Google Scholar 
[18] 
F. Hoppensteadt, "Mathematical Theories of Populations: Demographics, Genetics and Epidemics," Society for Industrial and Applied Mathematics, Philadelphia, PA, 1975. Google Scholar 
[19] 
M. Iannelli, M. Martcheva and F. A. Milner, "Genderstructured Population Modeling. Mathematical Methods, Numerics, and Simulations," Frontiers in Applied Mathematics, 31, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2005. Google Scholar 
[20] 
H. Inaba, "An Agestructured Twosex Model for Human Population Reproduction by First Marriage," volume 15 of Working paper series, Institute of Population Problems, Tokyo, 1993. Google Scholar 
[21] 
H. Inaba, Persistent age distributions for an agestructured twosex population model, Math. Population Studies, 7 (2000), 365398. Google Scholar 
[22] 
D. G. Kendall, Stochastic processes and population growth, J. Roy. Statist. Soc. Ser. B., 11 (1949), 230264. Google Scholar 
[23] 
M. Martcheva, Exponential growth in agestructured twosex populations, Math. Biosci., 157 (1999), 122. Google Scholar 
[24] 
M. Martcheva and F. A. Milner, A twosex agestructured population model: well posedness, Math. Population Stud., 7 (1999), 111129. Google Scholar 
[25] 
M. Martcheva and F. A. Milner, The mathematics of sex and marriage, revisited, Math. Population Stud., 9 (2001), 123141. Google Scholar 
[26] 
D. Maxin and F. Milner, The effect of nonreproductive groups on persistent sexually transmitted diseases, Math. Biosc. and Engin., 4 (2007), 505522. doi: 10.3934/mbe.2007.4.505. Google Scholar 
[27] 
F. Milner and K. Yang, The logistic, twosex, agestructured population model, J. Biol. Dyn., 3 (2009), 252270. Google Scholar 
[28] 
J. Prüss and W. Schappacher, Persistent agedistributions for a pairformation model, J. Math. Biol., 33 (1994), 1733. Google Scholar 
[29] 
G. F. Webb, "Structured Population Dynamics," Banach Center Publications, 63, Polish Acad. Sci., Warsaw, 2004. Google Scholar 
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