My scholarly interests include nonlinear analysis, differential and integral equations, mathematical ecology, fractal geometry, Polanyi’s theory of personal knowledge, and pedagogical tact. Select papers are linked below (* denotes HMC student co-author):
- A. Castro and J. Jacobsen, Radial Solutions to Elliptic Equations, Electronic Journal of Differential Equations, Special Issue in Honor of John W Neuberger, (2023), 87-100
- J. Jacobsen, Teaching from the Unknown, Journal of Humanistic Mathematics, Volume 11, Issue 1, January 2021
- J. Jacobsen, Y. Jin, M. A. Lewis, Integrodifference models for persistence in temporally varying river environments, Journal of Mathematical Biology, 70, (2015), 549-590.
- J. Jacobsen and T. McAdam*, A Boundary Value Problem for integrodifference population models with cyclic kernels, Discrete Contin Dyn Syst Ser B, 19 (10), (2014), 3191-3207.
- J. Jacobsen, Selling Mathematics: Service & Quality, Journal of Humanistic Mathematics, Volume 3, Issue 2, July 2013
- H. W. Mckenzie, Y. Jin, J. Jacobsen and M. A. Lewis, Râ‚€ Analysis of a Spatiotemporal Model for a Stream Population, SIAM Journal on Applied Dynamical Systems, 11 (2) , (2012), 567-596.
- J, Jacobsen, As Flat As Possible, SIAM Review, 49, (2007), 491-507.
- J. Jacobsen and K. Schmitt, The Liouville-Bratu-Gelfand Problem for Radial Operators, Journal of Differential Equations, 184, (2002), 283-298.
- J. Jacobsen and K. Schmitt, Radial Solutions of Quasilinear Elliptic Differential Equations, Handbook of Differential Equations, (2004), 359-435.
- V. Camacho*, R. Guy and J. Jacobsen, Traveling Waves and Shocks in a Viscoelastic Generalization of Burgers’ Equation, SIAM Journal on Applied Mathematics, 68 (5), (2008), 1316-1332.
- J. Jacobsen, O. Lewis*, B. Tennis*, Approximations of Continuous Newton’s Method: An Extension of Cayley’s Problem, Electronic Journal of Differential Equations, 15, (2007), 163-173.
- J. Jacobsen, A Liouville-Gelfand Equation for k-Hessian Operators, Rocky Mountain J. Math., Vol. 34 2, (2004), 665-684.
- J. Gjorgjieva* and J. Jacobsen, Turing Patterns on Growing Spheres: The Exponential Case, Discrete Contin. Dyn. Syst., (2007), Series A, suppl., p. 436-445. Note: There is an error in the diffusion-driven calculation in this paper as kindly pointed out by Madzvamuse et al.: See “Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains, J. Math Biol. (2010)” for an alternate approach to determining the diffusion-driven instability condition.