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On the existence of scattering solutions for the AbrahamLorentzDirac equation
1.  Dipartimento di Matematica, Via Saldini 50, Milano, IT20132, Italy 
[1] 
Thierry Horsin, Peter I. Kogut, Olivier Wilk. Optimal $L^2$control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions. Mathematical Control and Related Fields, 2016, 6 (4) : 595628. doi: 10.3934/mcrf.2016017 
[2] 
Guy V. Norton, Robert D. Purrington. The Westervelt equation with a causal propagation operator coupled to the bioheat equation.. Evolution Equations and Control Theory, 2016, 5 (3) : 449461. doi: 10.3934/eect.2016013 
[3] 
Yuan Li, ShouFu Tian. Inverse scattering transform and soliton solutions of an integrable nonlocal Hirota equation. Communications on Pure and Applied Analysis, 2022, 21 (1) : 293313. doi: 10.3934/cpaa.2021178 
[4] 
Changhun Yang. Scattering results for Dirac Hartreetype equations with small initial data. Communications on Pure and Applied Analysis, 2019, 18 (4) : 17111734. doi: 10.3934/cpaa.2019081 
[5] 
Yemin Chen. Analytic regularity for solutions of the spatially homogeneous LandauFermiDirac equation for hard potentials. Kinetic and Related Models, 2010, 3 (4) : 645667. doi: 10.3934/krm.2010.3.645 
[6] 
Marcel Braukhoff. Global analytic solutions of the semiconductor BoltzmannDiracBenney equation with relaxation time approximation. Kinetic and Related Models, 2020, 13 (1) : 187210. doi: 10.3934/krm.2020007 
[7] 
Sebastián Ferrer, Martin Lara. Families of canonical transformations by HamiltonJacobiPoincaré equation. Application to rotational and orbital motion. Journal of Geometric Mechanics, 2010, 2 (3) : 223241. doi: 10.3934/jgm.2010.2.223 
[8] 
Manuel de León, Juan Carlos Marrero, David Martín de Diego. Linear almost Poisson structures and HamiltonJacobi equation. Applications to nonholonomic mechanics. Journal of Geometric Mechanics, 2010, 2 (2) : 159198. doi: 10.3934/jgm.2010.2.159 
[9] 
Thierry Horsin, Peter I. Kogut. Optimal $L^2$control problem in coefficients for a linear elliptic equation. I. Existence result. Mathematical Control and Related Fields, 2015, 5 (1) : 7396. doi: 10.3934/mcrf.2015.5.73 
[10] 
Marcel Braukhoff. Semiconductor BoltzmannDiracBenney equation with a BGKtype collision operator: Existence of solutions vs. illposedness. Kinetic and Related Models, 2019, 12 (2) : 445482. doi: 10.3934/krm.2019019 
[11] 
Wenmin Gong, Guangcun Lu. On Dirac equation with a potential and critical Sobolev exponent. Communications on Pure and Applied Analysis, 2015, 14 (6) : 22312263. doi: 10.3934/cpaa.2015.14.2231 
[12] 
Shuji Machihara. One dimensional Dirac equation with quadratic nonlinearities. Discrete and Continuous Dynamical Systems, 2005, 13 (2) : 277290. doi: 10.3934/dcds.2005.13.277 
[13] 
Xiaoyan Lin, Xianhua Tang. Solutions of nonlinear periodic Dirac equations with periodic potentials. Discrete and Continuous Dynamical Systems  S, 2019, 12 (7) : 20512061. doi: 10.3934/dcdss.2019132 
[14] 
Yu Chen, Yanheng Ding, Tian Xu. Potential well and multiplicity of solutions for nonlinear Dirac equations. Communications on Pure and Applied Analysis, 2020, 19 (1) : 587607. doi: 10.3934/cpaa.2020028 
[15] 
Hartmut Pecher. Local wellposedness for the nonlinear Dirac equation in two space dimensions. Communications on Pure and Applied Analysis, 2014, 13 (2) : 673685. doi: 10.3934/cpaa.2014.13.673 
[16] 
Piero D'Ancona, Mamoru Okamoto. Blowup and illposedness results for a Dirac equation without gauge invariance. Evolution Equations and Control Theory, 2016, 5 (2) : 225234. doi: 10.3934/eect.2016002 
[17] 
Federico Cacciafesta, AnneSophie De Suzzoni. Weak dispersion for the Dirac equation on asymptotically flat and warped product spaces. Discrete and Continuous Dynamical Systems, 2019, 39 (8) : 43594398. doi: 10.3934/dcds.2019177 
[18] 
Noboru Okazawa, Kentarou Yoshii. Linear evolution equations with strongly measurable families and application to the Dirac equation. Discrete and Continuous Dynamical Systems  S, 2011, 4 (3) : 723744. doi: 10.3934/dcdss.2011.4.723 
[19] 
Lucas C. F. Ferreira, Jhean E. PérezLópez, Élder J. VillamizarRoa. On the product in BesovLorentzMorrey spaces and existence of solutions for the stationary Boussinesq equations. Communications on Pure and Applied Analysis, 2018, 17 (6) : 24232439. doi: 10.3934/cpaa.2018115 
[20] 
Alessio Pomponio. Oscillating solutions for prescribed mean curvature equations: euclidean and lorentzminkowski cases. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 38993911. doi: 10.3934/dcds.2018169 
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