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Hyperbolicelliptic models for wellreservoir flow
1.  International Research Institute of Stavanger, University of Stavanger, P.O. Box 8046, N4068 Stavanger, Norway 
2.  Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, N–0316 Oslo, Norway 
[1] 
Paola Goatin, Sheila Scialanga. Wellposedness and finite volume approximations of the LWR traffic flow model with nonlocal velocity. Networks & Heterogeneous Media, 2016, 11 (1) : 107121. doi: 10.3934/nhm.2016.11.107 
[2] 
Anouar Bahrouni. TrudingerMoser type inequality and existence of solution for perturbed nonlocal elliptic operators with exponential nonlinearity. Communications on Pure & Applied Analysis, 2017, 16 (1) : 243252. doi: 10.3934/cpaa.2017011 
[3] 
Zhiming Guo, ZhiChun Yang, Xingfu Zou. Existence and uniqueness of positive solution to a nonlocal differential equation with homogeneous Dirichlet boundary conditionA nonmonotone case. Communications on Pure & Applied Analysis, 2012, 11 (5) : 18251838. doi: 10.3934/cpaa.2012.11.1825 
[4] 
Tong Li, Kun Zhao. Global existence and longtime behavior of entropy weak solutions to a quasilinear hyperbolic blood flow model. Networks & Heterogeneous Media, 2011, 6 (4) : 625646. doi: 10.3934/nhm.2011.6.625 
[5] 
Florent Berthelin, Paola Goatin. Regularity results for the solutions of a nonlocal model of traffic flow. Discrete & Continuous Dynamical Systems, 2019, 39 (6) : 31973213. doi: 10.3934/dcds.2019132 
[6] 
. Adimurthi, Siddhartha Mishra, G.D. Veerappa Gowda. Existence and stability of entropy solutions for a conservation law with discontinuous nonconvex fluxes. Networks & Heterogeneous Media, 2007, 2 (1) : 127157. doi: 10.3934/nhm.2007.2.127 
[7] 
Alexander V. Rezounenko, Petr Zagalak. Nonlocal PDEs with discrete statedependent delays: Wellposedness in a metric space. Discrete & Continuous Dynamical Systems, 2013, 33 (2) : 819835. doi: 10.3934/dcds.2013.33.819 
[8] 
Keyan Wang. Global wellposedness for a transport equation with nonlocal velocity and critical diffusion. Communications on Pure & Applied Analysis, 2008, 7 (5) : 12031210. doi: 10.3934/cpaa.2008.7.1203 
[9] 
Zhaoquan Xu, Jiying Ma. Monotonicity, asymptotics and uniqueness of travelling wave solution of a nonlocal delayed lattice dynamical system. Discrete & Continuous Dynamical Systems, 2015, 35 (10) : 51075131. doi: 10.3934/dcds.2015.35.5107 
[10] 
Massimiliano Ferrara, Giovanni Molica Bisci, Binlin Zhang. Existence of weak solutions for nonlocal fractional problems via Morse theory. Discrete & Continuous Dynamical Systems  B, 2014, 19 (8) : 24832499. doi: 10.3934/dcdsb.2014.19.2483 
[11] 
Christos V. Nikolopoulos, Georgios E. Zouraris. Numerical solution of a nonlocal elliptic problem modeling a thermistor with a finite element and a finite volume method. Conference Publications, 2007, 2007 (Special) : 768778. doi: 10.3934/proc.2007.2007.768 
[12] 
N. V. Chemetov. Nonlinear hyperbolicelliptic systems in the bounded domain. Communications on Pure & Applied Analysis, 2011, 10 (4) : 10791096. doi: 10.3934/cpaa.2011.10.1079 
[13] 
YoungSam Kwon. On the wellposedness of entropy solutions for conservation laws with source terms. Discrete & Continuous Dynamical Systems, 2009, 25 (3) : 933949. doi: 10.3934/dcds.2009.25.933 
[14] 
Giuseppe Maria Coclite, Lorenzo Di Ruvo. A note on the convergence of the solution of the high order CamassaHolm equation to the entropy ones of a scalar conservation law. Discrete & Continuous Dynamical Systems, 2017, 37 (3) : 12471282. doi: 10.3934/dcds.2017052 
[15] 
Felisia Angela Chiarello, Paola Goatin. Nonlocal multiclass traffic flow models. Networks & Heterogeneous Media, 2019, 14 (2) : 371387. doi: 10.3934/nhm.2019015 
[16] 
Hongjie Dong, Doyoon Kim. Schauder estimates for a class of nonlocal elliptic equations. Discrete & Continuous Dynamical Systems, 2013, 33 (6) : 23192347. doi: 10.3934/dcds.2013.33.2319 
[17] 
Raffaella Servadei, Enrico Valdinoci. Variational methods for nonlocal operators of elliptic type. Discrete & Continuous Dynamical Systems, 2013, 33 (5) : 21052137. doi: 10.3934/dcds.2013.33.2105 
[18] 
Yuanhong Wei, Xifeng Su. On a class of nonlocal elliptic equations with asymptotically linear term. Discrete & Continuous Dynamical Systems, 2018, 38 (12) : 62876304. doi: 10.3934/dcds.2018154 
[19] 
Reinhard Racke, Jürgen Saal. Hyperbolic NavierStokes equations I: Local wellposedness. Evolution Equations & Control Theory, 2012, 1 (1) : 195215. doi: 10.3934/eect.2012.1.195 
[20] 
Antonio Greco, Vincenzino Mascia. Nonlocal sublinear problems: Existence, comparison, and radial symmetry. Discrete & Continuous Dynamical Systems, 2019, 39 (1) : 503519. doi: 10.3934/dcds.2019021 
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