Publications

J.A. Carrillo, H. Holden, S. Solem. Noise-driven bifurcations in a neural field system modelling networks of grid cells. Preprint available. (2021) arXiv:2109.07936 (Journal of Mathematical Biology, to appear)

K. Grunert and A. Reigstad. A regularised system for the nonlinear variational wave equation . Preprint available. (2020) arXiv:2008.13003

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.

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

M. Lewicka, N. Ubostad: A stability result for the Infinity-Laplace Equation. arxiv:1710.08635

E. Lindgren and P. Lindqvist: On Infinity Ground States in the Plane. To appear in Mathematical Research Letters. arxiv:2102.08869

M. Ehrnström, K. Nik and C. Walker. A direct construction of a full family of Whitham solitary waves. To appear in Proc. Amer. Math. Soc. Preprint available. 2022. arXiv:2204.03274.

M. Ehrnström, S. Walsh and C. Zeng. Smooth stationary water waves with exponentially localized vorticity. To appeaer in J. Eur. Math. Soc. (JEMS). Preprint avaiable. 2020. arXiv:1907.07335.

F. Hildrum and J. Xue. Periodic Hölder waves in a class of negative-order dispersive equations. Preprint available. 2022. arXiv:2202.07363.

O. I.H. Maehlen, J. Xue. One sided Hölder regularity of global weak solutions of negative order dispersive equations. Preprint available. 2021. arXiv:2107.01039.

D. S. Seth, K. Varholm, E. Wahlén. Symmetric doubly periodic gravity-capillary waves with small vorticity. Preprint available. 2022. arXiv:2204.13093.

A. Bressan, S.T. Galtung, K. Grunert, and K.T. Nguyen. Shock interactions for the Burgers-Hilbert equation.Comm. Partial Differential Equations.47:1795-1844, 2022. DOI, arXIv:2204.02421

K. Grunert and M. Tandy. Lipschitz stability for the Hunter-Saxton equation. J. Hyperbolic Differ. Equ. 19: 275-310, 2022. DOI, arXiv:2103.10227

S. T. Galtung and K. Grunert. Stumpons are non-conservative traveling waves of the Camassa-Holm equation. Phys. D 433, 133196, 2022. DOI,arXiv:2106.15443

K. Grunert and H. Holden. Uniqueness of conservative solutions for the Hunter–Saxton equation. Research in the Mathematical Sciences 9 Article no 9, 2022. DOI, arxiv

F. del Teso, J. Endal, and E. R. Jakobsen. Uniform tail estimates and Lp-convergence for finite-difference approximations of nonlinear diffusion equations. Discrete Contin. Dyn. Syst. (2022), DOI. arXiv:2202.02297.

I. Chowdhury, O. Ersland, and E. R. Jakobsen. On Numerical Approximations of Fractional and Nonlocal Mean Field Games. Found. Comput. Math. (2022), DOI, arXiv:2105.00073

F. del Teso, J. Endal, and M. Lewicka. On asymptotic expansions for the fractional infinity Laplacian. Asymptot. Anal., 127(3):201–216, 2022. DOI, arXiv

E. Lindgren and P. Lindqvist. On a comparison principle for Trudinger's equation. Adv. Calc. Var. 15, no 3, (2022), 401–415. DOI, arxiv: 1901.03591.

H. Holden, K. H. Karlsen, and P.H.C. Pang. Strong solutions of a stochastic differential equation with irregular random drift. Stochastic Process. Appl. 150:655-677, 2022. DOI, arXiv:2106.01790.

M. N. Arnesen. Decay and symmetry of solitary waves J. Math. Anal. Appl. 507:Paper No. 125450, 24, 2022. DOI, arXiv:1906.03407.

H. Le. Waves of maximal height for a class of nonlocal equations with inhomogeneous symbols Asymptot. Anal. 127:355-380, 2022. DOI, arXiv:2012.10558.

M. Ehrnström, M. D. Groves, and D. Nilsson. Existence of Davey-Stewartson Type Solitary Waves for the Fully Dispersive Kadomtsev-Petviashvilii equation SIAM J. Math. Anal. 54:4954-4986, 2022. DOI, arXiv:2110.03971.

M. Ehrnström and Y. Wang. Enhanced existence time of solutions to evolution equations of Whitham type. Discrete Contin. Dyn. Syst. 42:3841-3860, 2022. DOI, arXiv:2008.12722.

D. Nilsson. Extended lifespan of the fractional BBM equation. Aymptotic Analysis. 129:239-259, 2022. DOI, arXiv:1902.06336.

H. Holden, K.H. Karlsen, and P.H.C. Pang. The Hunter–Saxton equation with noise. Journal of Differential Equations 270 (2021) 725–786. journal, arXiv:2003.13984

G.M. Coclite, H. Holden, and N.H. Risebro. Singular diffusion with Neumann boundary conditions. Nonlinearity 34 (2021), 1633–1662. journal, arXiv:2004.12428

S. T. Galtung and K. Grunert. A numerical study of variational discretizations of the Camassa–Holm equation. BIT. 61:1271-1309, 2021. DOI,arXiv:2006.15562

K. Grunert and A. Reigstad. Traveling waves for the nonlinear variational wave equation.Partial Differ. Equ. Appl. 2:61, 2021. DOI, arXiv:2009.03178

K. Grunert, A. Nordli, and S. Solem. Numerical conservative solutions of the Hunter-Saxton equation. BIT 61:441-471, 2021. DOI, arXiv:2005.03882

O. Ersland and E. R. Jakobsen. On fractional and nonlocal parabolic Mean Field Games in the whole space. J. Differential Equations 301: 428-470, 2021. DOI

K. Grunert, H. Holden, E. R. Jakobsen, and N. C. Stenseth. Evolutionarily stable strategies in stable and periodically fluctuating populations: The Rosenzweig-MacArthur perdator-prey model. Proc. Natl. Acad. Sci. USA 118 (4), 2021. DOI

F. del Teso, J. Endal, and J. L. Vázquez. The one-phase fractional Stefan problem. Math. Models Methods Appl. Sci., 31(1):83–131, 2021. DOI, arXiv

E. Lindgren and P. Lindqvist. The Gradient Flow of Infinity-Harmonic Potentials. Advances in Mathematics 378, Paper no. 107526, 2021. DOI, arxiv:2006.15328.

G. Bruell and R.N. Dhara. Waves of maximal height for a class of nonlocal equations with homogeneous symbols. Indiana Univ. Math. J. 70:711-742, 2021. DOI, arXiv:1810.00248.

E. Dinvay and D. Nilsson. Solitary wave solutions of a Whitham-Boussinesq system. Nonlinear Anal. Real World Appl. 60:Paper No. 103280, 24, 2021. DOI, arXiv:1903.11292.

R.M. Colombo, H. Holden, and F. Marcellini. On the microscopic modeling of vehicular traffic on general networks. SIAM J. Appl. Math. 80 (2020), no. 3, 1377–1391. journal, arXiv:2002.09512

A. Bressan, S.T. Galtung, A. Reigstad, and J. Ridder. Competition models for plant stems. J. Differential Equations 269, 1571–1611, 2020. DOI, arXiv

J. A. Carrillo, K. Grunert, and H. Holden. A Lipschitz metric for the Camassa-Holm equation. Forum Math. Sigma, 8, e27, 292 pages (2020). DOI, arXiv:1904.02552

N. Alibaud, F. del Teso, J. Endal, and E. R. Jakobsen. The Liouville theorem and linear operators satisfying the maximum principle. J. Math. Pures Appl., 142: 229-242, 2020. DOI,arXiv:1907.02495

F. del Teso, J. Endal, and J. L. Vázquez. On the two-phase fractional Stefan problem. Adv. Nonlinear Stud., 20(2):437–458, 2020. DOI, arXiv

P. Lindqvist, M. Parviainen. A remark on infinite initial values for quasilinear parabolic equations. Nonlinear Analysis 194 (2020), 111391, DOI, arxiv:1811.11541.

F. Hoeg, P. Lindqvist. Regularity of solutions of the normalized p-Laplace equation. Advances Nonlinear Analysis 9 (2020), no. 1, 7-15. DOI, arxiv:1802.04568

K. Brustad, P. Lindqvist, and J. Manfredi. A discrete stochastic interpretation of the Dominative p-Laplace Equation. Differential and Integral Equations 33 (2020), 465-488. journal, arxiv:1809.00714.

F. Hildrum. Solitary waves in dispersive evolution equations of Whitham type with nonlinearities of mild regularity. Nonlinearity. 33:1594-1624, 2020. DOI, arXiv:1903.03354.

K. Varholm. Global bifurcation of waves with multiple critical layers. SIAM J. Math. Anal. 52:5066-5089, 2020. DOI, arXiv:1907.05736.

K. Varholm, E. Wahlén, and S. Walsh. On the stability of solitary water waves with a point vortex. Comm. Pure Appl. Math. 73:2634-2684, 2020. DOI, arXiv:1811.08024

H. Holden and N.H. Risebro. Models for dense multilane vehicular traffic. SIAM Journal on Mathematical Analysis 51 (5) (2019) 3694–3713. journal, arXiv:1812.01361

D. Stan, F. del Teso, J. Vazquez. Existence of weak solutions for a general porous medium equation with nonlocal pressure. Arch. Rational Mech. Anal., 233:451–496, 2019. arXiv, DOI

N. Cusimano, F. del Teso, L. Gerardo-Giorda. Numerical approximations for fractional elliptic equations via the method of semigroups. M2AN Math. Methods Numer. anal. DOI, arXiv

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, arXiv:1709.07743

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. doi, arXiv:1801.04121, jee.pdf.

E. Lindgren and P. Lindqvist. Infinity-Harmonic Potentials and their Streamlines. Discrete Contin. Dyn. Syst. 39, no. 8, 2019, 4731–4746. DOI, arxiv:1809.08130

D. Nilsson and Y. Wang. Solitary wave solutions to a class of Whitham-Boussinesq systems. Z. Angew. Math. Phys. 70, no. 13, 2019. DOI, arXiv:1810.03405

M. N. Arnesen. A non-local approach to waves of maximal height for the Degasperis-Procesi equation. J. Math. Anal. Appl. 479:25-44, 2019. DOI, arXiv:1808.08057

M. Ehrnström and Y. Wang. Enhanced existence time of solutions to the fractional Korteweg-de Vries equation. SIAM J. Math. Anal. 51:3298-3323, 2019. DOI, arxiv:1804.06297

M. Ehrnström and E. Wahlén. On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation. Ann. Inst. H. Poincaré C Anal. Non Linéaire 36:1603-1637, 2019. DOI, arXiv:1602.05384.

L, Pei and Y, Wang. A note on well-posedness of bidirectional Whitham equation. Appl. Math. Lett. 98:215-223, 2019 DOI, arXiv:1708.04551.

G. Bruell and R. Granero-Belinchón. On the the thin film Muskat and the thin film Stokes equations. J. Math. Fluid. Mech. 21:1422-6928, 2019. DOI, arXiv:1802.05509.

D. Nilsson and Y. Wang. Solitary wave solutions to a class of Whitham-Boussinesq systems. Z. Angew. Math. Phys. 70:Paper No. 70, 13, 2019. DOI, arXiv:1810.03405.

M. N Arnesen. Non-uniform dependence on initial data for equations of Whitham type. Adv. Differential Equations. 24:257-282, 2019. Journal Article, arXiv:1602.00250.

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. 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

U. S. Fjordholm and E. Wiedemann. Statistical solutions and Onsager's conjecture. Phys. D 376-377:259-265, 2018 DOI, arXiv:1706.04113.

A. Aasen and K. Varholm. Traveling gravity water waves with critical layers. J. Math. Fluid Mech. 20:161-187. 2018. DOI, arXiv:1508.04664.

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.

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

E. Lindgren and P. Lindqvist. Perron's Method and Wiener's Theorem for a Nonlocal Equation. Potential Analysis 46 no 4: pp. 705–737 (2017). arxiv:1603.09184

E. Lindgren and P. Lindqvist. 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

U. S. Fjordholm, S. Lanthaler and S. Mishra Statistical solutions of hyperbolic conservation laws: foundations. Arch. Ration. Mech. Anal. 226:809-849, 2017 DOI, arXiv:1605.05960

M. N. Arnesen. Existence of solitary-wave solutions to nonlocal equations. Discrete and Continuous Dynamical Systems, vol. 36(7), pp. 3483–3510 (2016). DOI, arXiv:1506.05256

K. Varholm, Solitary gravity-capillary water waves with point vortices. Discrete and Continuous Dynamical Systems, vol. 36(7), pp. 3927-3959 (2016). DOI, arXiv:1503.06143

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, arXiv:1406.6309

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). DOI, arXiv:1506.00475

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). DOI, arXiv:1409.0241

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). DOI arXiv:1401.4277

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