
Previous Article
The evolution thermistor problem under the WiedemannFranz law with metallic conduction
 DCDSB Home
 This Issue

Next Article
Firstorder entropies for the DerridaLebowitzSpeerSpohn equation
Modeling the indirect contamination of a structured population with continuous levels of exposure
1.  Department of Mathematics, Texas A&M University, College Station, TX 778433368, United States 
Mathematically, the problem consists of an advectionreaction partial differential equation with variable speed, coupled by mean of its boundary condition to an ordinary differential equation. Using a method of characteristics, we prove the global existence, uniqueness and nonnegativity of the mild solution to this system, and also the global boundedness of the total population when subjected to controlled growth dynamics such as socalled logistic behaviors.
[1] 
Út V. Lê. ContractionGalerkin method for a semilinear wave equation. Communications on Pure & Applied Analysis, 2010, 9 (1) : 141160. doi: 10.3934/cpaa.2010.9.141 
[2] 
ShuiHung Hou. On an application of fixed point theorem to nonlinear inclusions. Conference Publications, 2011, 2011 (Special) : 692697. doi: 10.3934/proc.2011.2011.692 
[3] 
G. Buffoni, S. Pasquali, G. Gilioli. A stochastic model for the dynamics of a stage structured population. Discrete & Continuous Dynamical Systems  B, 2004, 4 (3) : 517525. doi: 10.3934/dcdsb.2004.4.517 
[4] 
Fabrizio Colombo, Irene Sabadini, Frank Sommen. The inverse Fueter mapping theorem. Communications on Pure & Applied Analysis, 2011, 10 (4) : 11651181. doi: 10.3934/cpaa.2011.10.1165 
[5] 
Helge Dietert, Josephine Evans, Thomas Holding. Contraction in the Wasserstein metric for the kinetic FokkerPlanck equation on the torus. Kinetic & Related Models, 2018, 11 (6) : 14271441. doi: 10.3934/krm.2018056 
[6] 
Emile Franc Doungmo Goufo, Abdon Atangana. Dynamics of traveling waves of variable order hyperbolic Liouville equation: Regulation and control. Discrete & Continuous Dynamical Systems  S, 2018, 0 (0) : 645662. doi: 10.3934/dcdss.2020035 
[7] 
Li Yang, Zeng Rong, Shouming Zhou, Chunlai Mu. Uniqueness of conservative solutions to the generalized CamassaHolm equation via characteristics. Discrete & Continuous Dynamical Systems  A, 2018, 38 (10) : 52055220. doi: 10.3934/dcds.2018230 
[8] 
Roberto Camassa. Characteristics and the initial value problem of a completely integrable shallow water equation. Discrete & Continuous Dynamical Systems  B, 2003, 3 (1) : 115139. doi: 10.3934/dcdsb.2003.3.115 
[9] 
Alberto Bressan, Geng Chen, Qingtian Zhang. Uniqueness of conservative solutions to the CamassaHolm equation via characteristics. Discrete & Continuous Dynamical Systems  A, 2015, 35 (1) : 2542. doi: 10.3934/dcds.2015.35.25 
[10] 
Jeffrey W. Lyons. An application of an avery type fixed point theorem to a second order antiperiodic boundary value problem. Conference Publications, 2015, 2015 (special) : 775782. doi: 10.3934/proc.2015.0775 
[11] 
Mugen Huang, Moxun Tang, Jianshe Yu, Bo Zheng. A stage structured model of delay differential equations for Aedes mosquito population suppression. Discrete & Continuous Dynamical Systems  A, 2019, 0 (0) : 00. doi: 10.3934/dcds.2020042 
[12] 
Zhihua Liu, Hui Tang, Pierre Magal. Hopf bifurcation for a spatially and age structured population dynamics model. Discrete & Continuous Dynamical Systems  B, 2015, 20 (6) : 17351757. doi: 10.3934/dcdsb.2015.20.1735 
[13] 
Jacques Henry. For which objective is birth process an optimal feedback in age structured population dynamics?. Discrete & Continuous Dynamical Systems  B, 2007, 8 (1) : 107114. doi: 10.3934/dcdsb.2007.8.107 
[14] 
L. M. Abia, O. Angulo, J.C. LópezMarcos. Sizestructured population dynamics models and their numerical solutions. Discrete & Continuous Dynamical Systems  B, 2004, 4 (4) : 12031222. doi: 10.3934/dcdsb.2004.4.1203 
[15] 
Z.R. He, M.S. Wang, Z.E. Ma. Optimal birth control problems for nonlinear agestructured population dynamics. Discrete & Continuous Dynamical Systems  B, 2004, 4 (3) : 589594. doi: 10.3934/dcdsb.2004.4.589 
[16] 
Tristan Roget. On the longtime behaviour of age and trait structured population dynamics. Discrete & Continuous Dynamical Systems  B, 2019, 24 (6) : 25512576. doi: 10.3934/dcdsb.2018265 
[17] 
Li Wang, Yang Li, Liwei Zhang. A differential equation method for solving box constrained variational inequality problems. Journal of Industrial & Management Optimization, 2011, 7 (1) : 183198. doi: 10.3934/jimo.2011.7.183 
[18] 
Roberto Camassa, PaoHsiung Chiu, Long Lee, W.H. Sheu. A particle method and numerical study of a quasilinear partial differential equation. Communications on Pure & Applied Analysis, 2011, 10 (5) : 15031515. doi: 10.3934/cpaa.2011.10.1503 
[19] 
Li Jin, Hongying Huang. Differential equation method based on approximate augmented Lagrangian for nonlinear programming. Journal of Industrial & Management Optimization, 2017, 13 (5) : 115. doi: 10.3934/jimo.2019053 
[20] 
YuFeng Sun, Zheng Zeng, Jie Song. Quasilinear iterative method for the boundary value problem of nonlinear fractional differential equation. Numerical Algebra, Control & Optimization, 2019, 0 (0) : 00. doi: 10.3934/naco.2019045 
2018 Impact Factor: 1.008
Tools
Metrics
Other articles
by authors
[Back to Top]