{"id":872,"date":"2023-07-10T11:31:36","date_gmt":"2023-07-10T02:31:36","guid":{"rendered":"https:\/\/www.elst.okayama-u.ac.jp\/en\/?page_id=872"},"modified":"2025-01-22T14:54:30","modified_gmt":"2025-01-22T05:54:30","slug":"areas04_math","status":"publish","type":"page","link":"https:\/\/www.elst.okayama-u.ac.jp\/en\/education\/mc-suuri\/areas04_math\/","title":{"rendered":"Mathematical Analysis"},"content":{"rendered":"<h4>&nbsp;<\/h4>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-69 aligncenter\" src=\"https:\/\/www.elst.okayama-u.ac.jp\/up_load_files\/areas\/areas04_math\/theme_taniguchiG.png\" alt=\"\" width=\"519\" height=\"292\"><\/p>\n<p>Research Area &#8220;Mathematical Analysis&#8221; is devoted to theory on partial differential equations, theory of probability, functional analysis, dynamical systems and statistics.<\/p>\n<p>For theory on partial differential equations, we study multi-dimensional traveling fronts appearing in reaction-diffusion models in physics, chemistry and biology. For theory of probability, we study stochastic partial differential equations and their discrete models.<\/p>\n<table class=\"el_table_fix\" style=\"width: 100%\">\n<tbody>\n<tr>\n<th style=\"width: 20%\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/www.elst.okayama-u.ac.jp\/up_load_files\/areas\/areas04_math\/taniguchi-masaharu.jpg\" width=\"320\" height=\"408\"><\/th>\n<td style=\"width: 80%\">\n<ul>\n<li style=\"list-style-type: none;font-size: 12px;margin-left: -20px\"><span style=\"font-size: 12pt\">Prof. TANIGUCHI Masaharu<\/span><\/li>\n<li style=\"list-style-type: none;font-size: 12px;margin-left: -20px\"><span style=\"font-size: 12pt\">E-mail: taniguchi-m <span style=\"color: #0000ff\">[at]<\/span> okayama-u.ac.jp<\/span><\/li>\n<li style=\"list-style-type: none;font-size: 12px;margin-left: -20px\"><span style=\"font-size: 12pt\">partial differential equations, theory of probability, functional analysis, dynamical systems, statistics\n<p><\/span><\/li>\n<\/ul>\n<p><span style=\"font-size: 12pt\"><a class=\"el_linkBtn\" href=\"https:\/\/soran.cc.okayama-u.ac.jp\/html\/df7af8b0b5cb35f074506e4da22f6611_en.html\">Directory of Researchers<\/a> \u3000<a class=\"el_linkBtn\" href=\"https:\/\/www.math.okayama-u.ac.jp\/~taniguchi\/index-j.html\">Link to homepage<\/a><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<div style=\"width: 276px\" class=\"wp-caption alignright\"><a href=\"https:\/\/www.elst.okayama-u.ac.jp\/up_load_files\/areas\/areas04_math\/img_TANIGUCHI.png\"><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/www.elst.okayama-u.ac.jp\/up_load_files\/areas\/areas04_math\/img_TANIGUCHI.png\" alt=\"\" width=\"266\" height=\"203\"><\/a><p class=\"wp-caption-text\">Pyramidal traveling fronts in the Allen&#8211;Cahn equations<\/p><\/div>\n<p>For theory on partial differential equations, we study multi-dimensional traveling fronts in reaction-diffusion equations. We study V-form traveling fronts and pyramidal traveling fronts, axisymmetric traveling fronts, a traveling front whose cross section has a convex shape. Multi-dimensional traveling fronts describe propagation phenomena appearing in chemistry, physics and biology.<\/p>\n<table class=\"el_table_fix\" style=\"width: 100%\">\n<tbody>\n<tr>\n<th style=\"width: 20%\">&nbsp;<\/th>\n<td style=\"width: 80%\">\n<ul>\n<li style=\"list-style-type: none;font-size: 12px;margin-left: -20px\"><span style=\"font-size: 12pt\">Assoc. Prof. KAWAMOTO Masaki<\/span><\/li>\n<li style=\"list-style-type: none;font-size: 12px;margin-left: -20px\"><span style=\"font-size: 12pt\">E-mail: kawamoto.masaki<span style=\"color: #0000ff\"> [at]<\/span> okayama-u.ac.jp<\/span><\/li>\n<li style=\"list-style-type: none;font-size: 12px;margin-left: -20px\"><span style=\"font-size: 12pt\">Partial Differential Equations, Quantum Mechanics, Nonlinear Analysis\n<p><\/span><\/li>\n<\/ul>\n<p><span style=\"font-size: 12pt\"><a class=\"el_linkBtn\" href=\"https:\/\/soran.cc.okayama-u.ac.jp\/html\/b406ec7d394386cf8c2fc0f9228a80e5_en.html\">Directory of Researchers<\/a> \u3000<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>Quantum particles such as electrons are referred to as matter waves, and their motion does not conform to Newtonian mechanics. <br \/>\nTherefore, it is necessary to consider a different framework for understanding their motion, which is known as quantum mechanics.<br \/>\nThe mathematical analysis of quantum mechanics, incorporating functional analysis, saw significant development in the latter half of the 20th century. However, many open research problems still remain.<br \/>\nI am particularly engaged in research on the mathematical analysis of the Schr\u00f6dinger equation in electromagnetic fields.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp; Research Area &#8220;Mathematical Analysis&#8221; is devoted to theory on partial differential equation [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":0,"parent":140,"menu_order":47,"comment_status":"closed","ping_status":"closed","template":"template-layout_single.php","meta":{"footnotes":""},"class_list":["post-872","page","type-page","status-publish","hentry"],"aioseo_notices":[],"publishpress_future_action":{"enabled":false,"date":"2026-06-27 07:44:47","action":"change-status","newStatus":"draft","terms":[],"taxonomy":"","extraData":[]},"publishpress_future_workflow_manual_trigger":{"enabledWorkflows":[]},"_links":{"self":[{"href":"https:\/\/www.elst.okayama-u.ac.jp\/en\/wp-json\/wp\/v2\/pages\/872","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.elst.okayama-u.ac.jp\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.elst.okayama-u.ac.jp\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.elst.okayama-u.ac.jp\/en\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.elst.okayama-u.ac.jp\/en\/wp-json\/wp\/v2\/comments?post=872"}],"version-history":[{"count":8,"href":"https:\/\/www.elst.okayama-u.ac.jp\/en\/wp-json\/wp\/v2\/pages\/872\/revisions"}],"predecessor-version":[{"id":2447,"href":"https:\/\/www.elst.okayama-u.ac.jp\/en\/wp-json\/wp\/v2\/pages\/872\/revisions\/2447"}],"up":[{"embeddable":true,"href":"https:\/\/www.elst.okayama-u.ac.jp\/en\/wp-json\/wp\/v2\/pages\/140"}],"wp:attachment":[{"href":"https:\/\/www.elst.okayama-u.ac.jp\/en\/wp-json\/wp\/v2\/media?parent=872"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}