Publications

Preprints

  • N. Alibaud, F. del Teso, J. Endal, and E. R. Jakobsen. The Liouville theorem and linear operators satisfying the maximum principle. Submitted for publication. Preprint: https://arxiv.org/abs/1907.02495
  • J. A. Carrillo, K. Grunert, and H. Holden. A Lipschitz metric for the Camassa-Holm equation. Submitted for publication. (2019) arXiv:1904.02552
  • N. Alibaud, J. Endal, and E. R. Jakobsen. Optimal and dual stability results for L1 viscosity and L-infinity entropy solutions. Submitted for publication. (2018) arXiv:1812.02058
  • D. Stan, F. del Teso, J. Vazquez. Existence of weak solutions for a general porous medium equation with nonlocal pressure. To appear in ARMA arXiv:1609.05139
  • D. Nilsson and Y. Wang. Solitary wave solutions to a class of Whitham-Boussinesq systems. Submitted for publication. (2018) arXiv:1810.03405.
  • G. Bruell and R.N. Dhara. Waves of maximal height for a class of nonlocal equations with homogeneous symbols. Submitted for publication. (2018) arXiv:1810.00248.
  • G. Bruell and R. Granero-Belinchón. On the thin film Muskat and the thin film Stokes equations. Submitted for publication. (2018) arXiv:1802.05509.
  • M. N. Arnesen. A non-local approach to waves of maximal height for the Degasperis-Procesi equation. Submitted for publication. (2018) arXiv:1808.08057.
  • M. N. Arnesen. Non-uniform dependence on initial data for the Whitham equation. Under revision. (2016) arXiv:1602.00250.
  • M. Ehrnström and Y. Wang. Enhanced existence time of solutions to the fractional Korteweg-de Vries equation. Submitted for publication. (2018) arxiv:1804.06297.
  • L. Pei and Y. Wang, A conditional well-posedness result for the bidirectional Whitham equation. Submitted for publication. (2017). arXiv:1708.04551
  • M. Ehrnström and E. Wahlén. On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation. Accepted for publication in Ann. Inst. H. Poincaré Anal. Non Linéaire (2018). arXiv:1602.05384
  • U. S. Fjordholm, S. Lanthaler and S. Mishra. Statistical solutions of hyperbolic conservation laws I: Foundations. To appear in ARMA (2017). arXiv:1605.05960
  • U. S. Fjordholm and E. Wiedemann. Statistical solutions and Onsager's conjecture. Submitted for publication (2017). arXiv:1706.04113
  • N. Alibaud, F. del Teso, J. Endal, and E. R. Jakobsen. Characterization of nonlocal diffusion operators satisfying the Liouville theorem. Irrational numbers and subgroups of R^d. Preprint available, 2018. arXiv:1807.01843
  • K. Brustad, P. Lindqvist, J. Manfredi: A discrete interpretation of the Dominative p-Laplacian. arxiv:1809.00714
  • M. Lewicka, N. Ubostad: A stability result for the Infinity-Laplace Equation. arxiv:1710.08635
  • E. Lindgren, P. Lindqvist: Infinity-Harmonic Potentials and Their Streamlines. arxiv:1809.08130
  • P. Lindqvist, M. Parviainen: A remark on infinite initial values for quasilinear parabolic equations. To appear in Journal of Nonlinear Analysis. arxiv:1811.11541
  • E. Lindqren, P. Lindqvist: On a comparison principle for Trudinger's Equation. arxiv:1901.03591
  • F. Hoeg, P. Lindqvist: Regularity of solutions of the parabolic normalized p-Laplace equation. To appear in Advances Nonlinear Analysis 9 (2020), no. 1, 7-15. arxiv:1802.04568

Publications in 2019

  • E. R. Jakobsen, A. Picarelli, C. Reisinger. Improved order 1/4 convergence for piecewise constant policy approximation of stochastic control problems. Electon. Commun. Probab. DOI and arXiv:1901.01193
  • F. del Teso, J. Endal, and E. R. Jakobsen. Robust numerical methods for nonlocal (and local) equations of porous medium type. Part I: Theory. SIAM J. Numer. Anal. 57(5):2266–2299, 2019. DOI, arXiv
  • I. H. Biswas, I. Chowdhury, and E. R. Jakobsen. On the rate of convergence for monotone numerical schemes for nonlocal Isaacs equations. SIAM J. Numer. Anal. 57(2): 799-827, 2019. DOI
  • J. A. Carrillo, K. Grunert, and H. Holden. A Lipschitz metric for the Hunter-Saxton equation. Comm. Partial Differential Equations. 44(4): 309-334, 2019. DOI, arXiv:1612.02961
  • H. Hanche-Olsen, H. Holden, E.Malinnikova. An improvement of the Kolmogorov–Riesz compactness theorem. Expositiones Mathematicae 37 (2019) 84-91. DOI, arXiv:1705.01349v1
  • J. Kinnunen, P. Lehtela, P. Lindqvist, M. Parviainen. Supercaloric functions for the porous medium equation.J. Evol. Equ.19 no. 1: 249-270, 2019. jee.pdf.

Publications in 2018

  • L. Chen and E. R. Jakobsen. L1 semigroup generation for Fokker-Planck operators associated with general Levy driven SDEs. Discrete Contin. Dyn. Syst. 38(11): 5735-5763, 2018. DOI
  • L. Chen, E. R. Jakobsen, and A. Naess. On numerical density approximations of solutions of SDEs with unbounded coefficients. Adv. Comput. Math. 44(3): 693-721, 2018. DOI, arXiv:1506.05576
  • H.-L. Li, Y. Wang, and Z. Xin. Non-existence of classical solutions with finite energy to the Cauchy problem of the compressible Navier–Stokes equations Arch. Rational Mech. Anal. (2018). DOI.
  • H.-L. Li and Y. Wang. Formation of singularities of spherically symmetric solutions to the 3D compressible Euler equations and Euler-Poisson equations. Nonlinear Differ. Equ. Appl. 25 (2018). DOI.
  • K. Grunert and A. Nordli, Existence and Lipschitz stability for α-dissipative solutions of the two-component Hunter-Saxton system, J. Hyper. Differential Equations vol. 15 no 3 (2018) 559–597. DOI and arXiv:1610.05673
  • M. Grasmair, K. Grunert, H. Holden. On the equivalence of Eulerian and Lagrangian variables for the two-component Camassa–Holm system. On the equivalence of Eulerian and Lagrangian variables for the two-component Camassa-Holm system. Current research in nonlinear analysis 157–201, Springer Optim. Appl., 135, Springer, Cham, 2018. arXiv:1704.05289v1
  • K. Grunert and X. Raynaud. Symmetries and multipeakon solutions for the modified two-component Camassa-Holm system. EMS Series of Congress Reports: Non-Linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis. The Helge Holden Anniversary Volume (2018). DOI and arXiv:1704.06306
  • N. Cusimano, F. del Teso, L. Gerardo-Giorda, and G. Pagnini. Discretizations of the Spectral Fractional Laplacian on General Domains with Dirichlet, Neumann, and Robin Boundary Conditions. SIAM J. Numer. Anal. 56-3 (2018), pp. 1243-1272. DOI.
  • M. Ehrnström, M. A. Johnson and K. M. Claassen. Existence of a highest wave in a fully dispersive two-way shallow water model. Arch. Rational Mech. Anal. (2018). DOI and arXiv:1610.02603
  • M. Ehrnström and M.D. Groves. Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev–Petviashvili equation. Nonlinearity 31 (2018), 5351–5384. DOI and arXiv:1802.04823
  • M. Ehrnström and L Pei, Classical well-posedness in dispersive equations with nonlinearities of mild regularity, and a composition theorem in Besov spaces. J. Evol. Equ. DOI, arXiv:1709.04713
  • F. del Teso, J. Endal, and E. R. Jakobsen. On the well-posedness of solutions with finite energy for nonlocal equations of porous medium type. EMS Series of Congress Reports: Non-Linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis. The Helge Holden Anniversary Volume (2018). DOI, arXiv:1610.02221
  • F. del Teso, J. Endal, and E. R. Jakobsen. Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments. SIAM J. Numer. Anal., 56(6) (2018) 3611-3647. arXiv:1804.04985 DOI.
  • P. Lindqvist, D. Ricciotti. Regularity for an anisotropic equation in the plane.Nonlinear Analysis.177 (2018), pp. 628-636.arXiv:1801.08661
  • H. Holden and N. H. Risebro. Follow-the-Leader models can be viewed as a numerical approximation to the Lighthill–Whitham–Richards model for traffic flow. Networks and Heterogeneous Media 13(3) (2018) 409-421. DOI, arXiv:1702.01718
  • H. Holden and N. H. Risebro. The continuum limit of Follow-the-Leader models – a short proof. Discrete and Continuous Dynamical Systems 38(2) (2018) 715-722 DOI, arXiv:1709.07661

Publications in 2017

  • G. Bruell, M. Ehrnström, A. Geyer and L. Pei, Symmetric solutions of evolutionary partial differential equations. Nonlinearity, 30, no.10: pp 3932–3950 (2017). arXiv:1704.05483
  • G. Bruell, M. Ehrnström and L. Pei. Symmetry and decay of traveling wave solutions to the Whitham equation. J. Differential Equations 262(8): pp 4232–4254 (2017). arXiv:1608.07944
  • A. Aasen and K. Varholm, Traveling gravity water waves with critical layers. Journal of Mathematical Fluid Mechanics (2017). Online first
  • H. Kalisch and F. Remonato, Numerical bifurcation for the capillary Whitham equation. Physica D: Non-linear Phenomena, vol. 343, pp. 51-62 (2017). DOI
  • E. Chasseigne and E. R. Jakobsen. On nonlocal quasilinear equations and their local limits. J. Differential Equations 262(6): pp. 3759-3804 (2017). DOI, arXiv:1503.06939
  • F. del Teso, J. Endal, and E. R. Jakobsen. Uniqueness and properties of distributional solutions of nonlocal equations of porous medium type. Advances in Mathematics 305: pp. 78-143 (2017). DOI, arXiv:1507.04659
  • J. Eckhardt and K. Grunert. A Lagrangian view on complete integrability of the two-component Camassa-Holm system. J. Integrable Syst. 2:xyx002 (2017). DOI, arXiv:1605.05865
  • P. Lindqvist, E. Lindgren. Regularity of the p-Poisson Equation in the Plane. Journal d"Analyse Mathematique 132: pp. 217–228 (2017). arXiv:1311.6795
  • J. Eckhardt, F. Gesztesy, H. Holden, A. Kostenko, G. Teschl. Real-valued algebro-geometric solutions of the two-component Camassa–Holm hierarchy. Ann. Inst. Fourier (Grenoble) 67(3): 1185–1230 DOI, arXiv:1512.03956v1
  • P. Lindqvist. The time derivative in a singular parabolic equation. Differential and Integral Equations30, pp. 795–808 (2017). arXiv:1612.02301
  • F. del Teso, J. Endal, and E. R. Jakobsen. On distributional solutions of local and nonlocal problems of porous medium type. C. R. Acad. Sci. Paris, Ser. I, 355(11):1154–1160 (2017). DOI, arXiv:1706.05306

Publications in 2016

  • M. N. Arnesen. Existence of solitary-wave solutions to nonlocal equations. Discrete and Continuous Dynamical Systems, vol. 36(7), pp. 3483–3510 (2016). DOI
  • K. Varholm, Solitary gravity-capillary water waves with point vortices. Discrete and Continuous Dynamical Systems, vol. 36(7), pp. 3927-3959 (2016). DOI
  • T. Kuusi, P. Lindqvist and M. Parviainen. Shadows of Infinities. Annali di Matematica Pura ed Applicata, vol. 195 no 4, pp. 1185-1206 (2016). DOI
  • K. Grunert and K.T. Nguyen. On the Burgers–Poisson equation. J. Differential Equations, vol. 261 no 6, pp. 3220-3246 (2016). DOI, arXiv:1510.09144
  • K. Grunert. Solutions of the Camassa-Holm equation with accumulating breaking times. Dynamics of PDE, vol. 13 no 2, pp. 91-105 (2016). DOI, arXiv:1510.09014
  • J. Behrndt, F. Gesztesy, H. Holden, R. Nichols. Dirichlet-to-Neumann maps, abstract Weyl–Titchmarsh M-functions, and a generalized index of unbounded meromorphic operator-valued functions Journal of Differential Equations, vol 261, pp. 3551-3587 (2016) DOI, arXiv:1603.07089
  • R. Colombo and H. Holden. On the Braess paradox with nonlinear dynamics and control theory. Journal of Optimization Theory and Applications, vol. 168, pp. 216–230 (2016) DOI, arXiv:1703.09803
  • K. Grunert and H. Holden. The general peakon-antipeakon solution for the Camassa–Holm equation. Journal of Hyperbolic Differential Equations , vol. 13, pp. 353–380 (2016) DOI, arXiv:1502.07686v1
  • J. Kinnunen and P. Lindqvist. Unbounded supersolutions of some quasilinear parabolic equations. Nonlinear Analysis, vol 131, pp. 229-242 (2016).
  • P. Lindqvist and J. Manfredi. On the mean value property for the p-Laplace equation in the plane. Proc. Amer. Math. Soc., vol. 144 no 1, pp. 143-149 (2016).
  • J. Kinnunen, P. Lindqvist, and T. Lukkari. Perron's method for the porous medium equation. J. Eur. Math. Soc (JEMS), vol 18 no 12, pp. 2953-2969 (2016).
  • P. Lindqvist. Notes on the Infinity Laplace Equation. Springer Briefs in Mathematics, Bilbao 2016, Springer. DOI, arXiv:1411.1278
  • U. S. Fjordholm. Stability properties of the ENO method. Handbook of Numerical Methods for Hyperbolic Problems: Basic and Fundamental Issues, Volume 17, pp. 123-145 (2016). DOI, arXiv:1609.04178
2019-10-11, Jørgen Endal