{"id":150,"date":"2023-06-20T14:05:33","date_gmt":"2023-06-20T21:05:33","guid":{"rendered":"https:\/\/live-usc-dornsife.pantheonsite.io\/guillermo-reyes-souto\/?page_id=150"},"modified":"2023-06-20T14:05:48","modified_gmt":"2023-06-20T21:05:48","slug":"research","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/research\/","title":{"rendered":"Research"},"content":{"rendered":"\n\n \n \n\n\n\n\n\n\n\n
\n\n \n \n
\n\n \n

Research Interests<\/h2>\n
\n
    \n
  • Partial Differential Equations: Nonlinear diffusion equations, non-homogeneous media, semilinear elliptic problems, semigroups of operators and spectral theory.<\/li>\n
  • Mathematical Physics: Mechanics and Electromagnetic Theory. Lagrangian variational approach in Electromagnetics Theory.<\/li>\n
  • Consulting in Data Analysis and Machine Learning.<\/li>\n<\/ul>\n

     <\/p>\n

    List of Publications<\/h2>\n
    \n
      \n
    • J.A. Goldstein & G. Reyes, Equipartition of energy for an ill-posed system with cross fricton, in preparation.<\/li>\n<\/ul>\n
        \n
      • A. Castro & G. Reyes, Existence of multiple solutions for a semilinear problem and a counterexample by E. N. Dancer, submitted to Commun. Pure Appl. Analysis<\/li>\n<\/ul>\n
          \n
        • A. Figotin & G. Reyes, Lagrangian Variational Framework for Boundary Value Problems, J. Math. Phys.\u00a056<\/strong>, 093506 (2015)<\/li>\n<\/ul>\n
            \n
          • J.A. Goldstein, Gisele Ruiz Goldstein & G. Reyes, Overdamping and energy decay for abstract wave equations with strong damping, Asymptot. Anal.\u00a088<\/strong>\u00a0(4) (2014), pp 217-232.<\/li>\n<\/ul>\n
              \n
            • A. Figotin & G. Reyes, Multi-transmission-line-beam interactive system. Journal of Mathematical Physics\u00a054<\/strong>, 111901 (2013).<\/li>\n<\/ul>\n
                \n
              • R. G. Iagar, G. Reyes & A. Sanchez, Radial Equivalence of Nonhomogeneous Nonlinear Diffusion Equations, Acta Applicandae Mathematicae\u00a0123<\/strong>\u00a0(1) (2013), pp. 53-72.<\/li>\n<\/ul>\n
                  \n
                • J.A. Goldstein & G. Reyes, Equipartition of operator-weighted energies in damped wave equations, Asymptotic Analysis\u00a081<\/strong>\u00a0(2) (2013), pp. 171-187.<\/li>\n<\/ul>\n
                    \n
                  • A. de Pablo, G. Reyes & A. Sanchez, Blow-up for a nonhomogeneous heat equation with reaction, DCDS-A\u00a033<\/strong>\u00a0(2) (2013), pp. 643-662.<\/li>\n<\/ul>\n
                      \n
                    • S. Elena Nieto & G. Reyes, Asymptotic behavior of the solutions of the inhomogeneous Porous Medium Equation with critical vanishing density, Commun. Pure Appl. Anal.\u00a012<\/strong>\u00a0(2) (2013), pp. 1123-1139.<\/li>\n<\/ul>\n
                        \n
                      • S. Kamin, G. Reyes & J. L. Vazquez, Long time behavior for the inhomogeneous PME in a medium with rapidly decaying density, Discrete and Continuous Dynamical Systems, (special issue devoted to Nonlinear Parabolic Problems), DCDS-A\u00a026<\/strong>\u00a0(2) (2010), pp. 521-549.<\/li>\n<\/ul>\n
                          \n
                        • A. Bouzelmate, A. Gmira & G. Reyes, On the radial solutions of a degenerate elliptic equation with convection term, Int. J. Math. Anal. (Ruse)\u00a01<\/strong>\u00a0(2007), no. 17-20, pp. 975-993.<\/li>\n<\/ul>\n
                            \n
                          • A. Bouzelmate, A. Gmira & G. Reyes, On the self-similar solutions for a nonlinear Ornstein- Uhlenbeck equation, Electronic Journal of Differential Equations\u00a067<\/strong>\u00a0(2007), pp. 1-21.<\/li>\n<\/ul>\n
                              \n
                            • A. de Pablo, G. Reyes & A. Sanchez, Blow-up for a heat equation with convection and boundary flux, Proc. Roy. Soc. Edinburgh Sect. A\u00a0138<\/strong>\u00a0(3) (2008), pp. 513-530.<\/li>\n<\/ul>\n
                                \n
                              • G. Reyes & J. L. Vazquez, The inhomogeneous PME in several space dimensions. Existence and uniqueness of nite energy solutions, Commun. Pure Appl. Anal.\u00a07<\/strong>\u00a0(6) (2008), pp. 1275-1294.<\/li>\n<\/ul>\n
                                  \n
                                • G. Reyes & J. L. Vazquez, Long time behaviour for the inhomogeneous PME in a medium with slowly decaying density, Commun. Pure Appl. Anal.\u00a08<\/strong>\u00a0(2) (2009), pp 493-508.<\/li>\n<\/ul>\n
                                    \n
                                  • G. Reyes & J. L. Vazquez, The Cauchy problem for the inhomogeneous porous medium equation, Networks and Heterogeneous Media\u00a01<\/strong>\u00a0(2) (2006), pp. 337-351.<\/li>\n<\/ul>\n
                                      \n
                                    • G. Reyes & J. L. Vazquez, A weighted symmetrization for nonlinear elliptic and parabolic equations in inhomogeneous media, J. Eur. Math. Soc.\u00a08<\/strong>\u00a0(2006), pp. 531-554.<\/li>\n<\/ul>\n
                                        \n
                                      • G. Reyes & A. Tesei, Self-Similar Solutions of a Semilinear Parabolic Equation with Inverse-Square Potential, J. Differential Equations\u00a0219<\/strong>\u00a0(2005), pp. 40-77.<\/li>\n<\/ul>\n
                                          \n
                                        • L. Moschini, G. Reyes & A. Tesei, Nonuniqueness of solutions to a semilinear parabolic equation with inverse-square potential, Commun. Pure Appl. Anal.\u00a05<\/strong>\u00a0(1) (2006), pp. 155-179.<\/li>\n<\/ul>\n
                                            \n
                                          • R. Ferreira, A. de Pablo, G. Reyes & A. Sanchez, The interfaces of an inhomogeneous porous medium equation with convection, Comm. Partial Differential Equations\u00a031<\/strong>\u00a0(2006), pp. 1-18.<\/li>\n<\/ul>\n
                                              \n
                                            • A. de Pablo & G. Reyes, Long time behaviour for a nonlinear rst order equation, Nonlinear Anal.TMA\u00a065<\/strong>\u00a0(2) (2006), pp. 284-300.<\/li>\n<\/ul>\n
                                                \n
                                              • G. Reyes & A. Sanchez, Disappearance of interfaces for the porous medium equation with variable density and absorption, Asymptotic Analysis\u00a036<\/strong>\u00a0(2003), pp. 13-20.<\/li>\n<\/ul>\n
                                                  \n
                                                • G. Reyes & A. Tesei, Basic theory for a diffusion-absorption equation in an inhomogeneous medium, Nonlinear Differential Equations Appl.\u00a010<\/strong>\u00a0(2) (2003), pp. 197-222.<\/li>\n<\/ul>\n
                                                    \n
                                                  • R. Kersner, G. Reyes & A. Tesei, On a class of parabolic equations with variable density and absorption, Adv. Differential Equations\u00a07<\/strong>\u00a0(2) (2002), pp. 155-176.<\/li>\n<\/ul>\n
                                                      \n
                                                    • G. Reyes, Critical asymptotic behaviour for a perturbed conservation law, Asymptotic Analysis\u00a025<\/strong>\u00a0(2001), pp. 109-122.<\/li>\n<\/ul>\n
                                                        \n
                                                      • G. Reyes & J. L. Vazquez, Asymptotic behaviour for a generalized Burgers’ Equation, J. Math. Pures Appl.\u00a078<\/strong>\u00a0(1999), pp. 633-666.<\/li>\n<\/ul>\n
                                                          \n
                                                        • G. Reyes, Asymptotic behaviour of diffusion-convection processes, Nonlinear Anal.\u00a037<\/strong>\u00a0(1999), pp.301-318.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n\n\n\n<\/div>\n\n\n <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":370,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-150","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"\nResearch - Guillermo Reyes Souto<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/research\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Research - Guillermo Reyes Souto\" \/>\n<meta property=\"og:url\" content=\"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/research\/\" \/>\n<meta property=\"og:site_name\" content=\"Guillermo Reyes Souto\" \/>\n<meta property=\"article:modified_time\" content=\"2023-06-20T21:05:48+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/dornsife.usc.edu\\\/guillermo-reyes-souto\\\/research\\\/\",\"url\":\"https:\\\/\\\/dornsife.usc.edu\\\/guillermo-reyes-souto\\\/research\\\/\",\"name\":\"Research - Guillermo Reyes Souto\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/dornsife.usc.edu\\\/guillermo-reyes-souto\\\/#website\"},\"datePublished\":\"2023-06-20T21:05:33+00:00\",\"dateModified\":\"2023-06-20T21:05:48+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/dornsife.usc.edu\\\/guillermo-reyes-souto\\\/research\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/dornsife.usc.edu\\\/guillermo-reyes-souto\\\/research\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/dornsife.usc.edu\\\/guillermo-reyes-souto\\\/research\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/dornsife.usc.edu\\\/guillermo-reyes-souto\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Research\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/dornsife.usc.edu\\\/guillermo-reyes-souto\\\/#website\",\"url\":\"https:\\\/\\\/dornsife.usc.edu\\\/guillermo-reyes-souto\\\/\",\"name\":\"Guillermo Reyes Souto\",\"description\":\"USC Dornsife Guillermo Reyes Souto\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/dornsife.usc.edu\\\/guillermo-reyes-souto\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Research - Guillermo Reyes Souto","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/research\/","og_locale":"en_US","og_type":"article","og_title":"Research - Guillermo Reyes Souto","og_url":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/research\/","og_site_name":"Guillermo Reyes Souto","article_modified_time":"2023-06-20T21:05:48+00:00","twitter_card":"summary_large_image","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/research\/","url":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/research\/","name":"Research - Guillermo Reyes Souto","isPartOf":{"@id":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/#website"},"datePublished":"2023-06-20T21:05:33+00:00","dateModified":"2023-06-20T21:05:48+00:00","breadcrumb":{"@id":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/research\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/research\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/research\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/"},{"@type":"ListItem","position":2,"name":"Research"}]},{"@type":"WebSite","@id":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/#website","url":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/","name":"Guillermo Reyes Souto","description":"USC Dornsife Guillermo Reyes Souto","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"}]}},"_links":{"self":[{"href":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/wp-json\/wp\/v2\/pages\/150","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/wp-json\/wp\/v2\/users\/370"}],"replies":[{"embeddable":true,"href":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/wp-json\/wp\/v2\/comments?post=150"}],"version-history":[{"count":3,"href":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/wp-json\/wp\/v2\/pages\/150\/revisions"}],"predecessor-version":[{"id":153,"href":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/wp-json\/wp\/v2\/pages\/150\/revisions\/153"}],"wp:attachment":[{"href":"https:\/\/dornsife.usc.edu\/guillermo-reyes-souto\/wp-json\/wp\/v2\/media?parent=150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}