Publications

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

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

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.

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

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

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