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Advanced exercises on nonlinear difference differential equations and partial differential equations

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2014-12
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Solved exercises on nolinear partial differential equations and differential difference equations.
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[1] A Carpio Rodriguez, M Comte, R Lewandoski, A nonexistence result for a nonlinear equation involving critical Sobolev exponent, Annales de l'Institut Henri Poincaré - Analyse Non linéaire, 9(3), 243-261, 1992 [2] A. Carpio, Sharp estimates of the energy for the solutions of some dissipative second order evolution equations, Potential Analysis 1(3), 265-289, 1992 [3] A. Carpio, Existence de solutions globales rétrogrades pour des équations des ondes non linéaires dissipatives, Comptes rendus de l'Académie des sciences. Série 1, Mathématique, 316(8), 803-808, 1993 [4] A. Carpio, Comportement asymptotique des solutions des équations du tourbillon en dimensions 2 et 3, Comptes rendus de l'Académie des sciences. Série 1, Mathématique, 316(12), 1289-1294, 1993 [5] A. Carpio, Asymptotic behavior for the vorticity equations in dimensions two and three, Communications in partial differential equations 19 (5-6), 827-872, 1994 [6] A. Carpio, Unicite et comportement asymptotique pour des equations de convection-diffusion scalaires, Comptes rendus de l'Académie des sciences. Série 1, Mathématique 319 (1), 51-56, 1994 [7] A. Carpio, Comportement asymptotique dans les equations de Navier-Stokes, Comptes rendus de l'Académie des sciences. Série 1, Mathématique 319 (3), 223-228, 1994 [8] A. Carpio, Existence of global-solutions to some nonlinear dissipative wave-equations, Journal de mathématiques pures et appliquées 73 (5), 471-488, 1994 [9] A. Carpio, Large time behaviour in convection-diffusion equations, Annali della Scuola Normale Superiore di Pisa-Classe di Scienze 23 (3), 551-574, 1996 [10] A. Carpio, Large-time behavior in incompressible Navier-Stokes equations, SIAM Journal on Mathematical Analysis 27 (2), 449-475, 1996 [11] A Carpio, SJ Chapman, SD Howison, JR Ockendon, Dynamics of line singularities, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 355(1731), 2013-2024, 1997 [12] A. Carpio, Long‐time behaviour for solutions of the Vlasov-Poisson-Fokker- Planck equation, Mathematical methods in the applied sciences 21 (11), 985-1014, 1998 [13] A Carpio, SJ Chapman, On the modelling of instabilities in dislocation interactions, Philosophical Magazine B 78 (2), 155-157, 1998 [14] A Carpio, SJ Chapman, S Hastings, JB McLeod, Wave solutions for a discrete reaction-diffusion equation, European Journal of Applied Mathematics 11 (4), 399-412, 2000 [15] A Carpio, LL Bonilla, A Wacker, E Schöll, Wave fronts may move upstream in semiconductor superlattices, Physical Review E 61 (5), 4866, 2000 [16] A Carpio, P Hernando, M Kindelan, Numerical study of hyperbolic equations with integral constraints arising in semiconductor theory, SIAM Journal on Numerical Analysis 39 (1), 168-191, 2001 [17] A Carpio, SJ Chapman, JJL Velázquez, Pile-up solutions for some systems of conservation laws modelling dislocation interaction in crystals, SIAM Journal on Applied Mathematics 61 (6), 2168-2199, 2001 [18] A Carpio, LL Bonilla, Wave front depinning transition in discrete one-dimensional reaction-diffusion systems, Physical Review Letters 86 (26), 6034, 2001 [19] G Duro, A Carpio, Asymptotic profiles for convection–diffusion equations with variable diffusion, Nonlinear Analysis: Theory, Methods & Applications 45 (4), 407-433, 2001 [20] A Carpio, LL Bonilla, G Dell’Acqua, Motion of wave fronts in semiconductor superlattices, Physical Review E 64 (3), 036204, 2001 [21] A Carpio, E Cebrian, FJ Mustieles, Long time asymptotics for the semiconductor Vlasov-Poisson-Boltzmann equations, Mathematical Models and Methods in Applied Sciences 11 (09), 1631-1655, 2001 [22] A Carpio, LL Bonilla, A Luzón, Effects of disorder on the wave front depinning transition in spatially discrete systems, Physical Review E 65 (3), 035207, 2002 [23] A Carpio, Wavefronts for discrete two-dimensional nonlinear diffusion equations, Applied Mathematics Letters 15 (4), 415-421, 2002 [24] A Carpio, LL Bonilla, Depinning transitions in discrete reaction-diffusion equations, SIAM Journal on Applied Mathematics 63 (3), 1056-1082, 2003 [25] A Carpio, LL Bonilla, Pulse propagation in discrete systems of coupled excitable cells, SIAM Journal on Applied Mathematics 63 (2), 619-635, 2003 [26] A Carpio, LL Bonilla, Edge dislocations in crystal structures considered as traveling waves in discrete models, Physical Review Letters 90 (13), 135502, 2003 [27] A Carpio, LL Bonilla, Oscillatory wave fronts in chains of coupled nonlinear oscillators, Physical Review E 67 (5), 056621, 2003 [28] A Carpio, Nonlinear stability of oscillatory wave fronts in chains of coupled oscillators, Physical Review E 69 (4), 046601, 2004 [29] A Carpio, G Duro, Instability and collapse in discrete wave equations, Computational Methods in Applied Mathematics 5 (3), 223-241, 2005 [30] JC Neu, LL Bonilla, A Carpio, Igniting homogeneous nucleation, Physical Review E 71 (2), 021601, 2005 [31] A Carpio, LL Bonilla, Discrete models of dislocations and their motion in cubic crystals, Physical Review B 71 (13), 134105, 2005 [32] A Carpio, Asymptotic construction of pulses in the discrete Hodgkin-Huxley model for myelinated nerves, Physical Review E 72 (1), 011905, 2005 [33] A Carpio, Wave trains, self-oscillations and synchronization in discrete media, Physica D: Nonlinear Phenomena 207 (1-2), 117-136, 2005 [34] LL Bonilla, A Carpio, JC Neu, WG Wolfer, Kinetics of helium bubble formation in nuclear materials, Physica D: Nonlinear Phenomena 222 (1-2), 131-140, 2006 [35] LL Bonilla, A Carpio, I Plans, Dislocations in cubic crystals described by discrete models, Physica A: Statistical Mechanics and its Applications 376, 361-377, 2007 [36] I Plans, A Carpio, LL Bonilla, Homogeneous nucleation of dislocations as bifurcations in a periodized discrete elasticity model, EPL (Europhysics Letters) 81 (3), 36001, 2008 [37] A Carpio, ML Rapún, Topological derivatives for shape reconstruction, In: Bonilla, L.L. (eds) Inverse Problems and Imaging. Lecture Notes in Mathematics, vol 1943. Springer, Berlin, Heidelberg, 2008 [38] A Carpio, LL Bonilla, F de Juan, MAH Vozmediano, Dislocations in graphene, New Journal of Physics 10 (5), 053021, 2008 [39] A Carpio, ML Rapún, Solving inhomogeneous inverse problems by topological derivative methods, Inverse Problems 24 (4), 045014, 2008 [40] A Carpio, LL Bonilla, Periodized discrete elasticity models for defects in graphene, Physical Review B 78 (8), 085406, 2008 [41] A Carpio, ML Rapún, Domain reconstruction using photothermal techniques, Journal of Computational Physics 227 (17), 8083-8106, 2008 [42] JC Neu, A Carpio, LL Bonilla, Theory of surface deposition from boundary layers containing condensable vapour and particles, Journal of fluid mechanics 626, 183-210, 2009 [43] E Cebrián, LL Bonilla, A Carpio, Self-sustained current oscillations in the kinetic theory of semiconductor superlattices, Journal of Computational Physics 228 (20), 7689-7705, 2009 [44] A Carpio, G Duro, Explosive behavior in spatially discrete reaction-diffusion systems, Discrete Contin. Dyn. Syst. 12, 693-711, 2009 [45] I Plans, A Carpio, LL Bonilla, Toy nanoindentation model and incipient plasticity, Chaos, Solitons & Fractals 42 (3), 1623-1630, 2009 [46] A Carpio, ML Rapún, An iterative method for parameter identification and shape reconstruction, Inverse Problems in Science and Engineering 18 (1), 35-50, 2010 [47] A Carpio, BT Johansson, ML Rapún, Determining planar multiple sound-soft obstacles from scattered acoustic fields, Journal of Mathematical Imaging and Vision 36 (2), 185-199, 2010 [48] A Carpio, B Tapiador, Nonreflecting boundary conditions for discrete waves, Journal of Computational Physics 229 (5), 1879-1896, 2010 [49] A Prados, LL Bonilla, A Carpio, Phase transitions in a mechanical system coupled to Glauber spins, Journal of Statistical Mechanics: Theory and Experiment P06016, 2010 [50] LL Bonilla, A Prados, A Carpio, Nonequilibrium dynamics of a fast oscillator coupled to Glauber spins, Journal of Statistical Mechanics: Theory and Experiment P09019, 2010 [51] A Carpio, B Tapiador, Analysis of helium bubble growth in radioactive waste, Nonlinear Analysis: Real World Applications 11 (5), 4174-4184, 2010 [52] LL Bonilla, A Carpio, Theory of defect dynamics in graphene: defect groupings and their stability, Continuum Mechanics and Thermodynamics 23 (4), 337-346, 2011 [53] A Carpio, I Peral, Propagation failure along myelinated nerves, Journal of nonlinear science 21 (4), 499-520, 2011 [54] LL Bonilla, A Carpio, A Prados, RR Rosales, Ripples in a string coupled to Glauber spins, Physical Review E 85 (3), 031125, 2012 [55] LL Bonilla, A Carpio, Driving dislocations in graphene, Science 337 (6091), 161-162, 2012 [56] A Prados, A Carpio, LL Bonilla, Spin-oscillator model for the unzipping of biomolecules by mechanical force, Physical Review E 86 (2), 021919, 2012 [57] A Carpio, ML Rapún, Hybrid topological derivative and gradient-based methods for electrical impedance tomography, Inverse Problems 28 (9), 095010, 2012 [58] LL Bonilla, A Carpio, Ripples in a graphene membrane coupled to Glauber spins Journal of Statistical Mechanics: Theory and Experiment P09015, 2012 [59] LL Bonilla, A Carpio, Model of ripples in graphene, Physical Review B 86 (19), 195402, 2012 [60] D Rodriguez, B Einarsson, A Carpio, Biofilm growth on rugose surfaces, Physical Review E 86 (6), 061914, 2012 [61] A Prados, A Carpio, LL Bonilla, Sawtooth patterns in force-extension curves of biomolecules: An equilibrium-statistical-mechanics theory, Physical Review E 88 (1), 012704, 2013 [62] A Carpio, ML Rapún, Hybrid topological derivative-gradient based methods for nondestructive testing , Abstract and applied analysis 2013, 816134 [63] A Carpio, ML Rapún, Parameter identification in photothermal imaging, Journal of mathematical imaging and vision 49 (2), 273-288, 2014 [64] LL Bonilla, A Carpio, A Prados, Protein unfolding and refolding as transitions through virtual states, EPL (Europhysics Letters) 108 (2), 28002, 2014