Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion
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[1] T. Laurent,et al. Lp theory for the multidimensional aggregation equation , 2011 .
[2] Andrea L. Bertozzi,et al. Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups , 2004, SIAM J. Appl. Math..
[3] Wellposedness and regularity of solutions of an aggregation equation , 2010 .
[4] A. Ōkubo,et al. MODELLING SOCIAL ANIMAL AGGREGATIONS , 1994 .
[5] A. Bertozzi,et al. A Nonlocal Continuum Model for Biological Aggregation , 2005, Bulletin of mathematical biology.
[6] Jesús Rosado,et al. Uniqueness of Bounded Solutions to Aggregation Equations by Optimal Transport Methods , 2009 .
[7] Stephan Luckhaus,et al. Quasilinear elliptic-parabolic differential equations , 1983 .
[8] N. Risebro,et al. On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients , 2003 .
[9] J. Vázquez. The Porous Medium Equation , 2006 .
[10] C. Villani,et al. Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates , 2003 .
[11] R. Showalter. Monotone operators in Banach space and nonlinear partial differential equations , 1996 .
[12] G. M. Lieberman. SECOND ORDER PARABOLIC DIFFERENTIAL EQUATIONS , 1996 .
[13] R. Eftimiea,et al. Modeling Group Formation and Activity Patterns in Self-Organizing Collectives of Individuals , 2007 .
[14] G. Folland. Introduction to Partial Differential Equations , 1976 .
[15] Dong Li,et al. ON A NONLOCAL AGGREGATION MODEL WITH NONLINEAR DIFFUSION , 2009, 0902.2017.
[16] J. Carrillo,et al. Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations , 2011 .
[17] Martin Burger,et al. On an aggregation model with long and short range interactions , 2007 .
[18] Thomas Laurent,et al. Local and Global Existence for an Aggregation Equation , 2007 .
[19] Andrea L. Bertozzi,et al. Finite-time blow-up of L∞-weak solutions of an aggregation equation , 2010 .
[20] L. Ambrosio,et al. Gradient Flows: In Metric Spaces and in the Space of Probability Measures , 2005 .
[21] Andrea L. Bertozzi,et al. Finite-Time Blow-up of Solutions of an Aggregation Equation in Rn , 2007 .
[22] O. Ladyženskaja. Linear and Quasilinear Equations of Parabolic Type , 1968 .
[23] F. Otto. THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION , 2001 .
[25] Vincenzo Capasso,et al. Modeling the aggregative behavior of ants of the species Polyergus rufescens , 2000 .
[26] Dong Li,et al. Finite-Time Singularities of an Aggregation Equation in $${\mathbb {R}^n}$$ with Fractional Dissipation , 2009 .
[27] Ian Smith,et al. Introduction to Partial Differential Equations , 2006 .
[28] Andrea L. Bertozzi,et al. Blow-up in multidimensional aggregation equations with mildly singular interaction kernels , 2009 .
[29] N. Risebro,et al. CONVERGENCE OF FINITE DIFFERENCE SCHEMES FOR VISCOUS AND INVISCID CONSERVATION LAWS WITH ROUGH COEFFICIENTS , 2001 .
[30] Paul A. Milewski,et al. A simple model for biological aggregation with asymmetric sensing , 2008 .
[31] Augusto Visintin,et al. Strong convergence results related to strict convexity , 1984 .
[32] J. Carrillo. Entropy Solutions for Nonlinear Degenerate Problems , 1999 .
[33] Marion Kee,et al. Analysis , 2004, Machine Translation.
[34] J. Carrillo,et al. GLOBAL-IN-TIME WEAK MEASURE SOLUTIONS, FINITE-TIME AGGREGATION AND CONFINEMENT FOR NONLOCAL INTERACTION EQUATIONS , 2009 .
[35] D. Morale,et al. An interacting particle system modelling aggregation behavior: from individuals to populations , 2005, Journal of mathematical biology.
[36] Li Dong,et al. FINITE-TIME SINGULARITIES OF AN AGGREGATION EQUATION IN R WITH FRACTIONAL DISSIPATION , 2008 .
[37] Jose L. Rodrigo,et al. Refined blowup criteria and nonsymmetric blowup of an aggregation equation , 2009 .
[38] M. Bodnar,et al. An integro-differential equation arising as a limit of individual cell-based models , 2006 .
[39] Martin Burger,et al. Large time behavior of nonlocal aggregation models with nonlinear diffusion , 2008, Networks Heterog. Media.