{"id":35341,"date":"2025-02-12T13:09:51","date_gmt":"2025-02-12T12:09:51","guid":{"rendered":"https:\/\/www.uni.lu\/fstm-en\/?post_type=research-groups&#038;p=35341"},"modified":"2025-06-17T16:13:32","modified_gmt":"2025-06-17T14:13:32","slug":"research","status":"publish","type":"research-groups","link":"https:\/\/www.uni.lu\/fstm-en\/research-groups\/analysis-and-controllability-of-partial-differential-equations\/research\/","title":{"rendered":"Research"},"content":{"rendered":"<div class=\"section py-0 static\">\n<section class=\"py-0 wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\"><!-- SecondaryNavigationMirror --><div class=\"js-secondary-nav--sticky wp-block-unilux-blocks-secondary-navigation\" id=\"664371d6-d3ca-4871-adab-09c4c6ed839e\">\n    <nav id=\"secondary-navigation\" role=\"navigation\" aria-label=\"Secondary menu\" class=\"secondary-nav\">\n        <button class=\"secondary-nav__button btn btn-solid--primary w-full\" aria-expanded=\"false\" aria-controls=\"secondary-navigation__list\" title=\"The selected page is Research\" type=\"button\">\n            <span class=\"btn__name mr-auto\">Research<\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n                <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\" \/>\n            <\/svg>\n        <\/button>\n\n        <ul id=\"secondary-navigation__list\" class=\"secondary-nav__list\">\n            <li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/analysis-and-controllability-of-partial-differential-equations\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Overview<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/analysis-and-controllability-of-partial-differential-equations\/research\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link isactived\" aria-current=\"page\">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Research<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/analysis-and-controllability-of-partial-differential-equations\/people\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">People<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/analysis-and-controllability-of-partial-differential-equations\/join-us\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Join us<\/span>\n    <\/a>\n<\/li>\n        <\/ul>\n    <\/nav>\n<\/div>\n<!-- end SecondaryNavigationMirror --><\/div><\/section>\n\n\n\n<section class=\"wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\">\n<h1 class=\"has-text-align-left wp-block-unilux-blocks-heading\"        id=\"partial-differential-equations-and-modelling\"\n    >\nPartial Differential Equations and Modelling<\/h1>\n\n\n\n<p>Partial Differential Equations (PDEs) are equations where the unknown is a function\u2014or sometimes a vector field\u2014depending on several variables, often time and space. These equations involve one or more partial derivatives of the unknown.<\/p>\n\n\n\n<p>PDEs are ubiquitous in mathematically oriented scientific fields, including biology, physics, and engineering. On the theoretical side, key questions concern the existence, uniqueness, regularity, and stability of solutions. From a more applied perspective, an important challenge is to efficiently approximate solutions using numerical methods and computer simulations.<\/p>\n\n\n<figure class=\"wp-block-dev4-reusable-blocks-image  object-fit--cover\">\n    \n<img decoding=\"async\" class=\"wp-block-image unilux-custom-image-block\"\n                alt=\"\"\n            src=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2025\/02\/AdobeStock_1170570099_compressed-scaled.jpeg\"\n                srcset=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2025\/02\/AdobeStock_1170570099_compressed-300x168.jpeg 300w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2025\/02\/AdobeStock_1170570099_compressed-1024x574.jpeg 1024w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2025\/02\/AdobeStock_1170570099_compressed-768x430.jpeg 768w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2025\/02\/AdobeStock_1170570099_compressed-1536x861.jpeg 1536w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2025\/02\/AdobeStock_1170570099_compressed-2048x1148.jpeg 2048w\"\n                style=\"object-position: 50.00% 50.00%; font-family: &quot;object-fit: cover; object-position: 50.00% 50.00%;&quot;; aspect-ratio: 16\/9; object-fit: cover; width: 100%;\"\n        loading=\"lazy\"\n\/>    <\/figure><\/div><\/section>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Partial Differential Equations (PDEs) are equations where the unknown is a function\u2014or sometimes a vector field\u2014depending on several variables, often time and space. These equations involve one or more partial derivatives of the unknown.<\/p>\n","protected":false},"author":106,"featured_media":0,"parent":35325,"menu_order":1,"template":"","meta":{"featured_image_focal_point":{"x":0.62,"y":0.25},"show_featured_caption":false,"ulux_newsletter_groups":"","uluxPostTitle":"Analysis and controllability of Partial Differential Equations","uluxPrePostTitle":"Research Group","_trash_the_other_posts":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false},"field-of-interest":[294],"organisation":[65,29],"authorship":[106,131,133,132,130,223],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.3 (Yoast SEO v22.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Research - Analysis and controllability of Partial Differential Equations - FSTM research group I 91短视频<\/title>\n<meta name=\"description\" content=\"Partial Differential Equations (PDEs) are equations where the unknown is a function\u2014or sometimes a vector field\u2014depending on several variables, often time and space. These equations involve one or more partial derivatives of the unknown.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/analysis-and-controllability-of-partial-differential-equations\/research\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Research\" \/>\n<meta property=\"og:description\" content=\"Partial Differential Equations (PDEs) are equations where the unknown is a function\u2014or sometimes a vector field\u2014depending on several variables, often time and space. 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