S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary value conditions I, Comm. Pure Appl. Math, vol.12, pp.623-727, 1959.

L. Ambrosio, Geometric evolution problems, distance function and viscosity solutions, Calc. Var. Partial Differential Equations Springer, pp.5-93, 2000.

N. J. Armstrong, K. J. Painter, and J. A. Sherratt, A continuum approach to modelling cell-cell adhesion, J. Theoret. Biol, vol.243, pp.98-113, 2006.

D. G. Aronson, Density-dependent interaction-diffusion systems, Dynamics and Modelling of Reactive Systems (Proc. Adv, vol.44, pp.161-176, 1979.

C. Atkinson, G. E. Reuter, and C. J. Ridler-rowe, Traveling wave solution for some nonlinear diffu-sion equations, SIAM J. Math. Anal, vol.12, issue.6, pp.880-892, 1981.

P. C. Bailey, R. M. Lee, M. I. Vitolo, S. J. Pratt, E. Ory et al., Single-Cell Tracking of Breast Cancer Cells Enables Prediction of Sphere Formation from Early Cell Divisions, iScience, pp.29-39, 2018.

J. Bedrossian, N. Rodriguez, and A. L. Bertozzi, Local and global well-posedness for aggregation equations and Patlak-Keller-Segel models with degenerate diffusion, Nonlinearity, pp.1683-1714, 2011.

N. Bellomo, A. Bellouquid, J. Nieto, and J. Soler, On the asymptotic theory from microscopic to macroscopic growing tissue models: An overview with perspectives, Math. Models Methods Appl. Sci, vol.22, issue.01, p.1130001, 2012.

A. J. Bernoff and C. M. Topaz, A Primer of Swarm Equilibria, SIAM J. Appl. Dyn. Syst, vol.10, pp.212-250, 2011.

A. J. Bernoff and C. M. Topaz, Nonlocal aggregation models: A primer of swarm equilibria, SIAM Rev, vol.55, issue.4, pp.709-747, 2013.

A. L. Bertozzi and D. Slepcev, Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion, Comm. Pur. Appl. Anal, vol.9, pp.1617-1637, 2010.

A. L. Bertozzi, T. Laurent, and J. Rosado, L p theory for the multidimensional aggregation equation, Comm. Pur. Appl. Math, vol.64, pp.45-83, 2011.

A. L. Bertozzi, J. B. Garnett, and T. Laurent, Characterization of radially symmetric finite time blowup in multidimensional aggregation equations, SIAM J. Math. Anal, vol.44, pp.651-681, 2012.

M. Berstch, D. Hilhorst, H. Izuhara, and M. Mimura, A nonlinear parabolichyperbolic system for contact inhibition of cell-growth, Differ. Equations Appl, vol.4, issue.1, pp.137-157, 2012.

M. Bertsch, D. Hilhorst, H. Izuhara, M. Mimura, and T. Wakasa, Travelling wave solutions of a parabolic-hyperbolic system for contact inhibition of cell-growth, Eur. J. Appl. Math, vol.26, issue.03, pp.297-323, 2015.

P. Billingsley, Convergence of Probability Measures, 1999.

M. Bodnar and J. J. Velazquez, An integro-differential equation arising as a limit of individual cell-based models, J. Differential Equations, vol.222, pp.341-380, 2006.

M. Burger and M. D. Francesco, Large time behaviour of nonlocal aggregation models with nonlinear diffusion, Netw. Heterog. Media, vol.3, pp.749-785, 2008.

M. Burger, R. Fetecau, and Y. Huang, Stationary states and asymptotic behavior of aggregation models with nonlinear local repulsion, SIAM J. Appl. Dyn. Syst, vol.13, issue.1, pp.397-424, 2014.

H. Byrne and D. Drasdo, Individual-based and continuum models of growing cell populations: a comparison, J. Math. Biol, vol.58, issue.4-5, pp.657-687, 2009.

V. Calvez and Y. Dolak-struß, Asymptotic behavior of a two-dimensional Keller-Segel model with and without density control, In Mathematical Modeling of Biological Systems, vol.II, pp.323-337, 2008.

V. Calvez, L. Corrias, and M. A. Ebde, Blow-up, concentration phenomenon and global existence for the Keller-Segel model in high dimension, Comm. Partial Differential Equations, vol.37, issue.4, pp.561-584, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00462450

R. S. Cantrell, C. Cosner, and Y. Lou, Approximating the ideal free distribution via reaction-diffusion-advection equations, J. Differential Equations, vol.245, issue.12, pp.3687-3703, 2008.

V. Capasso and D. Morale, Asymptotic behavior of a system of stochastic particles subject to nonlocal interactions, Stochastic Anal. Appl, vol.27, issue.3, pp.574-603, 2009.

J. A. Carrillo, Y. P. Choi, and S. P. Perez, A review on attractive-repulsive hydrodynamics for consensus in collective behavior, Active Particles, vol.1, pp.259-298, 2017.

J. A. Carrillo, H. Murakawa, M. Sato, H. Togashi, and O. Trush, A population dynamics model of cell-cell adhesion incorporating population pressure and density saturation, J. Theor. Biol, vol.474, pp.14-24, 2019.

C. Castaing, P. Raynaud-de-fitte, and M. Valadier, Young Measures on Topological Spaces: with Applications in Control Theory and Probability Theory, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00726642

T. Cazenave and A. Haraux, An Introduction to Semilinear Evolution Equations, Oxford Lect. Ser. Math. Appl, vol.13, 1998.

M. G. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues, Journal of Functional Analysis, vol.8, issue.2, pp.321-340, 1971.

M. G. Crandall and P. H. Rabinowitz, The Hopf bifurcation theorem in infinite dimensions, Arch. Rational Mech. Anal, vol.67, issue.1, pp.53-72, 1977.

K. C. Chang, Methods in nonlinear analysis, 2006.

S. N. Chow and K. Lu, Invariant manifolds and foliations for quasiperiodic systems, J. Differential Equations, vol.117, pp.1-27, 1995.

J. H. Cushman, B. X. Hu, and F. W. Deng, Nonlocal reactive transport with physical and chemical heterogeneity: Localization errors, Water Resources Research, vol.31, issue.9, pp.2219-2237, 1995.

C. Dahmann, A. C. Oates, and M. Brand, Boundary formation and maintenance in tissue development, Nat. Rev. Genet, vol.12, issue.1, p.43, 2011.

A. De-pablo and J. L. Vázquez, Travelling waves and finite propagation in a reactiondiffusion equation, J. Differential Equations, vol.93, issue.1, pp.19-61, 1991.

A. H. Delgoshaie, D. W. Meyer, P. Jenny, and H. A. Tchelepi, Non-local formulation for multiscale flow in porous media, Journal of Hydrology, vol.531, pp.649-654, 2015.

Y. Du, F. Quiros, and M. Zhou, Logarithmic corrections in Fisher-KPP type, Porous Medium Equations, 2018.

A. Ducrot, F. L. Foll, P. Magal, H. Murakawa, J. Pasquier et al., An in Vitro Cell Population Dynamics Model Incorporating Cell Size, Quiescence, and Contact Inhibition, Math. Model. Methods Appl. Sci, vol.21, issue.supp01, p.871, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00992222

A. Ducrot and P. , Asymptotic behaviour of a non-local diffusive logistic equation, SIAM J. Math. Anal, vol.46, pp.1731-1753, 2014.

A. Ducrot, X. Fu, and P. , Turing and Turing-Hopf bifurcations for a reaction diffusion qquation with nonlocal advection, J. Nonlinear Sci, vol.28, issue.5, pp.1959-1997, 2018.

R. M. Dudley, Convergence of Baire measures, pp.251-268, 1966.

J. Dyson, S. A. Gourley, R. Villella-bressan, and G. F. Webb, Existence and asymptotic properties of solutions of a nonlocal evolution equation modeling cell-cell adhesion, SIAM J. Math. Anal, vol.42, issue.4, pp.1784-1804, 2010.

R. Eftimie, G. Vries, M. A. Lewis, and F. Lutscher, Modeling group formation and activity patterns in self-organizing collectives of individuals, Bull. Math. Biol, vol.69, pp.1537-1565, 2007.

B. Engquist and S. Osher, One-sided difference approximations for nonlinear conservation laws, Math. Comp, vol.36, issue.154, pp.321-351, 1981.

L. C. Evans, Partial differential equations, 1998.

B. Fiedler and P. Polácik, Complicated dynamics of scalar reaction diffusion equations with a nonlocal term, Proc. Royal Soc. Edinburgh, pp.263-276, 1990.

R. L. Foote, Regularity of the distance function, Proc. Amer. Math. Soc, vol.92, issue.1, pp.153-155, 1984.

X. Fu and P. , Asymptotic behavior of a nonlocal advection system with two populations, 2018.

X. Fu, Q. Griette, and P. , A cell-cell repulsion model on a hyperbolic Keller-Segel equation, 2019.

D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics. U.S. Government Printing Office, 2001.

W. S. Gurney and R. M. Nisbet, The regulation of inhomogeneous populations, J. Theoret. Biol, vol.52, pp.441-457, 1975.

F. Hamel and C. Henderson, Propagation in a Fisher-KPP equation with non-local advection, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01580261

M. Haragus and G. Iooss, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01325715

B. D. Hassard, N. D. Kazarinoff, and Y. Wan, Theory and Applications of Hopf Bifurcaton, 1981.

D. Henry, Geometric Theory of Semilinear Parabolic Equation, Lecture Notes in Mathematics, vol.840, 1981.

T. Hillen, K. J. Painter, and C. Schmeiser, Global existence for chemotaxis with finite sampling radius, Discrete Contin, Dyn. Syst. Ser. B, vol.7, issue.1, pp.125-144, 2007.

T. Hillen and K. J. Painter, A user's guide to PDE models for chemotaxis, J. Math. Biol, vol.58, issue.1-2, pp.183-217, 2009.

T. Hillen, K. J. Painter, and M. Winkler, Convergence of a cancer invasion model to a logistic chemotaxis model, Math. Models Methods Appl. Sci, vol.23, pp.165-198, 2013.

M. W. Hirsch, S. Smale, and R. L. Devaney, Differential equations, dynamical systems, and an introduction to chaos, 2012.

E. E. Holmes, M. A. Lewis, J. E. Banks, and R. R. Veit, Partial differential equations in ecology: spatial interactions and population dynamics, Ecology, vol.75, issue.1, pp.17-29, 1994.

D. Horstmann, From 1970 until present: the Keller-Segel model in chemotaxis and its consequences, J. Jahresberichte DMV, vol.105, issue.3, pp.103-165, 2003.

X. Hu and J. H. Cushman, Nonequilibrium statistical mechanical derivation of a nonlocal Darcy's law for unsaturated/saturated flow, Stochastic Hydrology and Hydraulics, vol.8, pp.109-116, 1994.

R. Huang, C. Jin, M. Mei, and J. Yin, Existence and stability of traveling waves for degenerate reaction-diffusion equation with time delay, J. Nonlinear Sci, vol.28, issue.3, pp.1011-1042, 2018.

S. Katsunuma, H. Honda, T. Shinoda, Y. Ishimoto, T. Miyata et al., Synergistic action of nectins and cadherins generates the mosaic cellular pattern of the olfactory epithelium, J. Cell Biol, vol.212, issue.5, pp.561-575, 2016.

K. Kawasaki, Diffusion and the formation of spatial distribution, Mathematical Sciences, vol.16, pp.47-52, 1978.

E. F. Keller and L. A. Segel, Model for chemotaxis, J. Theor. Biol, vol.30, pp.225-234, 1971.

R. J. Leveque, Finite volume methods for hyperbolic problems, 2002.

A. J. Leverentz, C. M. Topaz, and A. J. Bernoff, Asymptotic dynamics of attractiverepulsive swarms, SIAM J. Appl. Dyn. Syst, vol.8, pp.880-908, 2009.

Y. Lou and W. M. Ni, Diffusion, self-diffusion and cross-diffusion, J. Differential Equations, vol.131, issue.1, pp.79-131, 1996.

Y. Lou and W. M. Ni, Diffusion vs cross-diffusion: an elliptic approach, J. Differential Equations, vol.154, issue.1, pp.157-190, 1999.

A. Lunardi, Analytic semigroups and optimal regularity in parabolic problems, 2012.

P. Magal and S. Ruan, On semilinear Cauchy problems with non-dense domain, Adv. Differential Equations, vol.14, issue.11, pp.1041-1084, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00441244

P. Magal and S. Ruan, Theory and Applications of Abstract Semilinear Cauchy Problems, vol.201, 2018.

M. Mimura and K. Kawasaki, Spatial segregation in competitive interaction-diffusion equations, J. Math. Biol, vol.9, issue.1, pp.49-64, 1980.

A. Mogilner and L. Edelstein-keshet, A nonlocal model for a swarm, J. Math. Biol, vol.38, pp.534-570, 1999.

A. Mogilner, L. Edelstein-keshet, L. Bent, and A. Spiros, Mutual interactions, potentials, and individual distance in a social aggregation, J. Math. Biol, vol.47, pp.353-389, 2003.

D. Morale, V. Capasso, and K. Oelschläger, An interacting particle system modelling aggregation behaviour: from individuals to populations, J. Math. Biol, vol.50, pp.49-66, 2005.

S. Motsch and D. Peurichard, From short-range repulsion to Hele-Shaw problem in a model of tumor growth, J. Math. Biol, vol.76, pp.205-234, 2018.

H. Murakawa and H. Togashi, Continuous models for cell-cell adhesion, J. Theor. Biol, vol.372, pp.1-12, 2015.

J. D. Murray, Mathematical Biology I: An Introduction, volume I, 2003.

J. D. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications, vol.II, 2003.

G. Nadin, B. Perthame, and L. Ryzhik, Traveling waves for the Keller-Segel system with Fisher birth terms, Interfaces Free Bound, vol.10, issue.4, pp.517-538, 2008.

T. Nagai and M. Mimura, Asymptotic behaviour for a nonlinear degenerate diffusion equation in population dynamics, SIAM J. Appl. Math, vol.43, pp.449-464, 1983.

K. Oelschläger, A law of large numbers for moderately interacting diffusion processes, Z. Wahrsch. Verw. Gebiete, vol.69, pp.279-322, 1985.

K. Oelschläger, Large systems of interacting particles and the porous medium equation, J. Differential Equations, pp.294-346, 1990.

K. J. Painter, J. M. Bloomfield, J. A. Sherratt, and A. Gerisch, A nonlocal model for contact attraction and repulsion in heterogeneous cell populations, Bull. Math. Biol, vol.77, issue.6, pp.1132-1165, 2015.

C. S. Patlak, Random walk with persistence and external bias, Bull. Math. Biophys, vol.15, pp.311-338, 1953.

J. Pasquier, L. Galas, C. Boulangé-lecomte, D. Rioult, F. Bultelle et al., Different modalities of intercellular membrane exchanges mediate cell-to-cell glycoprotein transfers in MCF-7 breast cancer cells, J. Biol. Chem, vol.287, issue.10, pp.7374-7387, 2012.
URL : https://hal.archives-ouvertes.fr/hal-02314806

J. Pasquier, P. Magal, C. Boulangé-lecomte, G. F. Webb, and F. L. Foll, Consequences of cell-to-cell P-glycoprotein transfer on acquired multidrug resistance in breast cancer: a cell population dynamics model, Biol. Direct, vol.6, issue.1, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01738512

B. Perthame and A. L. Dalibard, Existence of solutions of the hyperbolic Keller-Segel model, Trans. Amer. Math. Soc, vol.361, pp.2319-2335, 2009.

G. , Non-local interaction equations: stationary states and stability analysis, Differential Integral Equations, vol.25, pp.417-440, 2012.

K. P. Rybakowski, An abstract approach to smoothness of invariant manifolds, Appl. Anal, vol.49, issue.1-2, pp.119-150, 1993.

M. Sen and E. Ramos, A spatially non-local model for flow in porous media. Transport in porous media, vol.92, pp.29-39, 2012.

D. Serre, Systèmes de lois de conservation II, Diderot Editeur Arts et Sciences, 1996.

N. Shigesada, K. Kawasaki, and E. Teramoto, Spatial segregation of interacting species, J. Theoret. Biol, vol.79, issue.1, pp.83-99, 1979.

J. Smoller, Shock waves and reaction-diffusion equations, vol.258, 1983.

Y. Song, S. Wu, and H. Wang, Spatiotemporal dynamics in the single population model with memory-based diffusion and nonlocal effect, J. Differential Equations, 2019.

R. L. Sutherland, R. E. Hall, and I. W. Taylor, Cell proliferation kinetics of MCF-7 human mammary carcinoma cells in culture and effects of tamoxifen on exponentially growing and plateau-phase cells, Cancer research, vol.43, issue.9, pp.3998-4006, 1983.

H. B. Taylor, A. Khuong, Z. Wu, Q. Xu, R. Morley et al., Cell segregation and border sharpening by Eph receptorephrin-mediated heterotypic repulsion, J. Royal Soc. Interface, vol.14, issue.132, p.20170338, 2017.

R. Temam, Infinite-dimensional dynamical systems in mechanics and physics

E. F. Toro, Riemann solvers and numerical methods for fluid dynamics: a practical introduction, 2013.

M. Valadier, Methods of nonconvex analysis, pp.152-188, 1446.

A. Vanderbauwhede and G. Iooss, Center manifold theory in infinite dimensions, vol.1, pp.125-163, 1992.

J. L. Vázquez, The Porous Medium Equation: Mathematical Theory, 2007.

A. Yagi, Abstract Parabolic Evolution Equations and their Applications, 2010.

M. L. Zeeman, Extinction in competitive Lotka-Volterra systems, Proc. Amer. Math. Soc, vol.123, issue.1, pp.87-96, 1995.