{"id":389,"date":"2020-01-05T18:40:13","date_gmt":"2020-01-05T18:40:13","guid":{"rendered":"https:\/\/math.hmc.edu\/jacobsen\/?page_id=389"},"modified":"2026-03-25T13:12:11","modified_gmt":"2026-03-25T13:12:11","slug":"research","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/jacobsen\/research\/","title":{"rendered":"Publications"},"content":{"rendered":"\n<p>My scholarly interests include nonlinear analysis, differential and integral equations, mathematical ecology, fractal geometry, Polanyi&#8217;s theory of personal knowledge, and pedagogical tact.<\/p>\n\n\n\n<p>Selected Publications (* denotes HMC student co-author):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/link.springer.com\/article\/10.1007\/s00283-026-10512-7\">In Praise of Acoustic Mathematics<\/a>, Math Intelligencer (2026)<\/li>\n\n\n\n<li><a href=\"https:\/\/ejde.math.txstate.edu\/special\/02\/c2\/castro.pdf\" data-type=\"link\" data-id=\"https:\/\/ejde.math.txstate.edu\/special\/02\/c2\/castro.pdf\">Radial Solutions to Elliptic Equations<\/a>, (with A. Castro), <em>Electronic Journal of Differential Equations, Special Issue in Honor of John W Neuberger<\/em>, (2023), 87-100<\/li>\n\n\n\n<li><a href=\"https:\/\/scholarship.claremont.edu\/jhm\/vol11\/iss1\/15\/\">Teaching from the <\/a><a href=\"https:\/\/scholarship.claremont.edu\/cgi\/viewcontent.cgi?article=1690&amp;context=jhm\">Unknown<\/a>, <em>Journal of Humanistic Mathematics<\/em>, Volume 11, Issue 1, January 2021<\/li>\n\n\n\n<li><a href=\"https:\/\/link.springer.com\/article\/10.1007\/s00285-014-0774-y\">Integrodifference models for persistence in temporally varying river environments<\/a>,&nbsp;<em>(with Y. Jin and M. Lewis), Journal of Mathematical Biology<\/em>,&nbsp;<strong>70<\/strong>, (2015), 549-590.<\/li>\n\n\n\n<li><a href=\"https:\/\/www.ma.utexas.edu\/images\/MATH\/graduate-publications\/jj_tm_cyclic_kernels.pdf\">A Boundary Value Problem&nbsp;for integrodifference population models with cyclic kernels<\/a>, (with T. McAdam*), Discrete Contin Dyn Syst Ser B, <strong>19 (10), <\/strong>(2014), 3191-3207.<\/li>\n\n\n\n<li><a href=\"https:\/\/scholarship.claremont.edu\/cgi\/viewcontent.cgi?article=1123&amp;context=jhm\">Selling Mathematics: Service &amp; Quality<\/a>, <em>Journal of Humanistic Mathematics<\/em>, Volume 3, Issue 2, July 2013<\/li>\n\n\n\n<li><a href=\"https:\/\/scholarship.claremont.edu\/cgi\/viewcontent.cgi?article=1768&amp;context=hmc_fac_pub\">R\u2080 Analysis of a Spatiotemporal Model for a Stream Population<\/a>, (with H. Mckenzie,&nbsp;Y. Jin, and M. Lewis), <em>SIAM Journal on Applied Dynamical Systems<\/em>,&nbsp;<strong>11 (2)&nbsp;<\/strong>, (2012), 567-596.<\/li>\n\n\n\n<li><a href=\"https:\/\/scholarship.claremont.edu\/cgi\/viewcontent.cgi?article=1767&amp;context=hmc_fac_pub\">As Flat As Possible<\/a>, SIAM Review, <strong>49<\/strong>, (2007), 491-507.<\/li>\n\n\n\n<li><a href=\"https:\/\/scholarship.claremont.edu\/cgi\/viewcontent.cgi?article=1771&amp;context=hmc_fac_pub\">The Liouville-Bratu-Gelfand Problem for Radial Operators<\/a>, (with K. Schmitt), Journal of Differential Equations, <strong>184<\/strong>, (2002), 283-298.<\/li>\n\n\n\n<li><a href=\"https:\/\/math.hmc.edu\/jacobsen\/wp-content\/uploads\/sites\/9\/2020\/01\/Canada-A.-Drabek-P.-Fonda-A.-eds.-Handbook-of-differential-equations.-Ordinary-differential-equations.-Vol.1-Elsevier-2004ISBN-0444511288709s_MCde_.pdf\">Radial Solutions of Quasilinear Elliptic Differential Equations<\/a>, (with K. Schmitt), Handbook of Differential Equations, (2004), 359-435.<\/li>\n\n\n\n<li><a href=\"https:\/\/scholarship.claremont.edu\/cgi\/viewcontent.cgi?article=1769&amp;context=hmc_fac_pub\">Traveling Waves and Shocks in a Viscoelastic Generalization of Burgers&#8217; Equation<\/a>, (with V. Camacho* and R. Guy), SIAM Journal on Applied Mathematics, <strong>68<\/strong> <strong>(5)<\/strong>, (2008), 1316-1332.<\/li>\n\n\n\n<li><a href=\"https:\/\/scholarship.claremont.edu\/cgi\/viewcontent.cgi?article=1765&amp;context=hmc_fac_pub\">Approximations of Continuous Newton&#8217;s Method: An Extension of Cayley&#8217;s Problem<\/a>, (with O. Lewis* and B. Tennis*), Electronic Journal of Differential Equations, <strong>15<\/strong>, (2007), 163-173.<\/li>\n\n\n\n<li><a href=\"https:\/\/scholarship.claremont.edu\/cgi\/viewcontent.cgi?article=1764&amp;context=hmc_fac_pub\">Turing Patterns on Growing Spheres: The Exponential Case<\/a>, (with J. Gjorgjieva*), Discrete Contin. Dyn. Syst., (2007), Series A, suppl., p. 436-445. <strong>Note:<\/strong> There is an error in the diffusion-driven calculation in this paper as kindly pointed out by Madzvamuse et al.: See &#8220;Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains, J. Math Biol. (2010)&#8221; for an alternate approach to determining the diffusion-driven instability condition.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>My scholarly interests include nonlinear analysis, differential and integral equations, mathematical ecology, fractal geometry, Polanyi&#8217;s theory of personal knowledge, and pedagogical tact. Selected&#8230;<\/p>\n","protected":false},"author":23,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[],"class_list":["post-389","page","type-page","status-publish","hentry"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/jacobsen\/wp-json\/wp\/v2\/pages\/389","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hmc.edu\/jacobsen\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.hmc.edu\/jacobsen\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/jacobsen\/wp-json\/wp\/v2\/users\/23"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/jacobsen\/wp-json\/wp\/v2\/comments?post=389"}],"version-history":[{"count":26,"href":"https:\/\/math.hmc.edu\/jacobsen\/wp-json\/wp\/v2\/pages\/389\/revisions"}],"predecessor-version":[{"id":844,"href":"https:\/\/math.hmc.edu\/jacobsen\/wp-json\/wp\/v2\/pages\/389\/revisions\/844"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/jacobsen\/wp-json\/wp\/v2\/media?parent=389"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/jacobsen\/wp-json\/wp\/v2\/tags?post=389"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}