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Jørgen Endal

Photo © Kristine Graneng (2017)
Associate professor // Førsteamanuensis


	Upcoming events To top	Organizing: TBA Attending: TBA
	Contact To top	Email: jorgen (dot) endal (at) ntnu (dot) no Office: Room 1152, SBII, Alfred Getz vei 1, Gløshaugen, Trondheim Address: Department of Mathematical Sciences, NTNU, NO-7491 Trondheim
	CV To top	CV (not updated). See also ORCID.
	Affiliation To top	Department of Mathematical Sciences
	Research To top	Nonlinear (integro-)partial differential equations. Common features: local or nonlocal (anomalous/Lévy type) diffusion, nonlinear convection and/or diffusion Main equations of interest: scalar conservation laws, convection-diffusion equations, diffusion equations of porous medium type, Hamilton-Jacobi-Bellman equations Concept of solutions: distributional/very weak solutions, energy solutions, entropy solutions, viscosity solutions Mathematical properties studied: regularity, asymptotic behaviour, well-posedness, stability, continuous dependence, approximation
	Publications To top	Click to see submitted for publication/pending publication (sorted by date): [1] N. Alibaud, J. Endal, E. R. Jakobsen, and O. Mæhlen. Nonlocal degenerate parabolic hyperbolic equations on bounded domains. Submitted, 2023. [arXiv] [journal] Click to see publications in refereed journals (sorted by date): [15] N. Alibaud, J. Endal, and E. R. Jakobsen. Optimal stability results and nonlinear duality for $L^{1}$ viscosity and $L^{∞}$ entropy solutions. To appear in Journal de Mathématiques Pures et Appliquées, 2024. [arXiv] [journal] [14] J. Endal, L. I. Ignat, and F. Quirós. Heat equations with fast convection: source-type solutions and large-time behaviour. Discrete Contin. Dyn. Syst. Ser. S, 17(4):1497–1512, 2024. [arXiv] [journal] [13] J. Endal, L. I. Ignat, and F. Quirós. Large-time behaviour for anisotropic stable nonlocal diffusion problems with convection. J. Math. Pures Appl. (9), 179:277–336, 2023. [arXiv] [journal] [12] F. del Teso, J. Endal, Espen R. Jakobsen, and J. L. Vázquez. Evolution driven by the infinity fractional Laplacian. Calc. Var., 62:136, 2023. [arXiv] [journal] [11] M. Bonforte and J. Endal. Nonlocal nonlinear diffusion equations. Smoothing effects, Green functions, and functional inequalities. J. Funct. Anal., 284(6):109831, 2023. [arXiv] [journal] [10] F. del Teso, J. Endal, and E. R. Jakobsen. Uniform tail estimates and $L^{p}$ ( $R^{N}$ )-convergence for finite-difference approximations of nonlinear diffusion equations. Discrete Contin. Dyn. Syst., 43(3&4):1319–1346, 2023. [arXiv] [journal] [9] F. del Teso, J. Endal, and M. Lewicka. On asymptotic expansions for the fractional infinity Laplacian. Asymptot. Anal., 127(3):201–216, 2022. [arXiv] [journal] [8] F. del Teso, J. Endal, and J. L. Vázquez. The one-phase fractional Stefan problem. Math. Models Methods Appl. Sci., 31(1):83–131, 2021. [arXiv] [journal] [7] N. Alibaud, F. del Teso, J. Endal, and E. R. Jakobsen. The Liouville theorem and linear operators satisfying the maximum principle. J. Math. Pures Appl. (9), 142:229–242, 2020. [arXiv] [journal] [6] F. del Teso, J. Endal, and J. L. Vázquez. On the two-phase fractional Stefan problem. Adv. Nonlinear Stud., 20(2):437–458, 2020. [arXiv] [journal] [5] F. del Teso, J. Endal, and E. R. Jakobsen. Robust numerical methods for nonlocal (and local) equations of porous medium type. Part I: Theory. SIAM J. Numer. Anal., 57(5):2266–2299, 2019. [arXiv] [journal] [4] F. del Teso, J. Endal, and E. R. Jakobsen. Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments. SIAM J. Numer. Anal., 56(6):3611–3647, 2018. [arXiv] [journal] [3] F. del Teso, J. Endal, and E. R. Jakobsen. On distributional solutions of local and nonlocal problems of porous medium type. C. R. Acad. Sci. Paris, Ser. I, 355(11):1154–1160, 2017. [arXiv] [journal] [2] F. del Teso, J. Endal, and E. R. Jakobsen. Uniqueness and properties of distributional solutions of nonlocal equations of porous medium type. Adv. Math., 305:78–143, 2017. [arXiv] [journal] [1] J. Endal and E. R. Jakobsen. $L^{1}$ Contraction for Bounded (Nonintegrable) Solutions of Degenerate Parabolic Equations. SIAM J. Math. Anal., 46(6):3957–3982, 2014. [arXiv] [journal] Click to see publications in refereed conference proceedings (sorted by date): [1] F. del Teso, J. Endal, and E. R. Jakobsen. On the well-posedness of solutions with finite energy for nonlocal equations of porous medium type. In Non-Linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis, EMS Ser. Congr. Rep., pages 129–168. Eur. Math. Soc., Zürich, 2018. [arXiv] [journal] Click to see unpublished preprints (sorted by date): [1] N. Alibaud, F. del Teso, J. Endal, and E. R. Jakobsen. Characterization of nonlocal diffusion operators satisfying the Liouville theorem. Irrational numbers and subgroups of $R^{d}$ . Preprint, 2018. [arXiv] [journal] See also arXiv, Google Scholar, or Research Gate.
	Grants & Awards To top	A research stay in Bucharest for two weeks during the summer of 2023. Funded by Research in Pairs in Bucharest (RiPB). Top-up financing of outgoing MSCA fellows for 24 months starting September 1 2020. Funded by Research Council of Norway. Marie Skłodowska-Curie Actions – Individual Fellowship (H2020-MSCA-IF-2018) for 24 months starting September 1 2020. Funded by European Union's Horizon 2020 Research and Innovation Programme. Click for more info: Project title: Novel techniques for quantitative behaviour of convection-diffusion equations (techFRONT). Understanding natural processes through partial differential equations. Description: Physical laws are mathematically encoded into Partial Differential Equations (PDEs). They tell us how certain quantities – like heat, water, or cars – depend on position and time. Precise information on the fundamental processes of the natural world is based to a large extent on PDEs; in turn, these processes will hint at solutions to mathematical problems. The EU-funded techFRONT project will study fine properties of irregular solutions of certain PDEs. Project research will seek to answer if initially irregular solutions become regular after some time, and if the PDEs are well-posed for growing (large) initial data. It will also investigate how solutions behave in the most quantitative way, by using explicit barriers or by understanding the long-time behaviour of the PDEs. FRINATEK Personal Overseas Research Grant for 6 months in 2019. Funded by Research Council of Norway. The Dimitris N. Chorafas Foundation Award (nominated by NTNU in 2018). Click for more info: The Dimitris N. Chorafas Foundation awards scientific prizes for outstanding work in selected fields in the engineering sciences, medicine and the natural sciences. It rewards research characterized by its high potential for practical application and by the special significance attached to its aftermath. Every year, partner universities in Europe, North America and Asia evaluate the research work of their graduating doctorate students and propose the best for prizing. Fellowship grant for 1.5 months in 2016 as part of the research programme Interactions between Partial Differential Equations & Functional Inequalities. Institut Mittag-Leffler (IML), Stockholm, Sweden.
	Theses To top	Doctoral thesis: On degenerate parabolic problems with local and nonlocal diffusion, NTNU, September 2017. Advisor: Prof. E. R. Jakobsen. Master's thesis: Nonlinear fractional convection-diffusion equations, with nonlocal and nonlinear fractional diffusion, NTNU, June 2013. Advisor: Prof. E. R. Jakobsen.
	Research stays To top	Summer 2023 (June 19–30): Research in Pairs Bucharest, Bucharest, Romania. Research stay for 2 weeks (invited by Liviu Ignat). Click to see 2014–2022: Spring 2022 (May 23–February 27): Université de Tours (UnivTours), Tours, France. Research stay for 1 week (invited by Boris Andreianov). Spring 2022 (May 17–February 22): Université Paris Dauphine (Dauphine), Paris, France. Research stay for 1 week (invited by Jean Dolbeault). Spring 2020 (February 23–February 28): Universidad Complutense de Madrid (UCM), Madrid, Spain. Research stay for 1 week (invited by Félix del Teso). Fall 2019 (September 15–September 20): Université de Tours (UnivTours), Tours, France. Research stay for 1 week (invited by Boris Andreianov). Spring 2019 (February 4–February 12): Basque Center for Applied Mathematics (BCAM), Bilbao, Spain. Research stay for 1.5 weeks (invited by Félix del Teso). Spring 2019 (January 8–June 30): Universidad Autónoma de Madrid (UAM), Madrid, Spain. Research stay for 6 months (invited by Matteo Bonforte). Spring 2018 (June 30–July 7): University of Pittsburgh (Pitt), Pittsburgh, Pennsylvania, US. Research stay for 1 week (invited by Marta Lewicka). Spring 2018 (May 03–May 12): Université de Bourgogne Franche-Comté (UBFC), Besançon, France. Research stay for 1.5 weeks (invited by Nathaël Alibaud). Spring 2018 (March 19–March 23): Universidad Autónoma de Madrid (UAM), Madrid, Spain. Research stay for 1 week (invited by Matteo Bonforte). Fall 2016 (November 06–December 16): Institut Mittag-Leffler (IML), Stockholm, Sweden. Fellowship grant for 1.5 months as part of the research programme Interactions between Partial Differential Equations & Functional Inequalities. Spring 2016 (February 01–June 26): Université de Bourgogne Franche-Comté (UBFC), Besançon, France. Research stay for 5 months (invited by Nathaël Alibaud). Fall 2015 (September 01–December 18): École Normale Supérieure (ENS), Paris, France. Research stay for 4 months (invited by Cyril Imbert).
	Talks & Posters To top	Summer 2023 (June 26–27): Nonlocal nonlinear diffusion equations. Smoothing effects, Green functions, and functional inequalities, Workshop on PDEs, Bucharest, Romania. Click to see 2014–2022: Fall 2022 (November 23): Ildkula etter en kjernefysisk eksplosjon, Onsdagsseminar, Seminar, Trondheim, Norway. Summer 2022 (June 10): Nonlocal nonlinear diffusion equations. Smoothing effects, Green functions, and functional inequalities, 2nd Norwegian meeting on PDEs, Conference, Bergen, Norway. Spring 2022 (March 04): Nonlocal nonlinear diffusion equations. Smoothing effects, Green functions, and functional inequalities, Seminario doble de ecuaciones en derivadas parciales, Seminar, UAM, Spain. Spring 2022 (January 18): Instantaneous boundedness in linear and nonlinear diffusion equations, and related functional inequalities, Congreso Bienal de la Real Sociedad Matemática Española (RSME 2022), Conference, Ciudad Real, Spain. Spring 2021 (June 15): From PhD to Post Doc, NTNU PhD Seminar, Seminar, Online. Spring 2021 (May 5): The one-phase fractional Stefan problem, Online Analysis and PDE seminar, Seminar, Online. Spring 2020 (February 24): The one-phase fractional Stefan problem, 2nd IMI one-day workshop on PDEs, Workshop, Madrid, Spain. Spring 2020 (February 19): The one-phase fractional Stefan problem, DNA seminar, NTNU, Trondheim, Norway. Spring 2020 (January 27): Connections between $L^{1}$ -solutions of Hamilton-Jacobi-Bellman equations and $L^{∞}$ -solutions of convection-diffusion equations, V Congreso de Jovénes Investigadores Castelló 2020 (JOVENESRSME 2020), Conference, Castelló, Spain. Fall 2019 (September 19): On nonlocal (and local) equations of porous medium type. Background, analysis, and numerical simulations, Seminar, UnivTours, Tours, France. Fall 2019 (September 12): Life as a PhD candidate, Introduction seminar for PhD candidates at NTNU, Trondheim, Norway. Spring 2019 (June 18): Nonlocal (and local) nonlinear diffusion equations. Background, analysis, and numerical approximation, The Mathematics of Finite Elements and Applications 2019 (MAFELAP 2019), Conference, London, UK. Spring 2019 (June 07): Connections between $L^{1}$ -solutions of Hamilton-Jacobi-Bellman equations and $L^{∞}$ -solutions of convection-diffusion equations, Norwegian meeting on PDEs, Conference, Trondheim, Norway. Spring 2019 (May 24): Connections between $L^{1}$ -solutions of Hamilton-Jacobi-Bellman equations and $L^{∞}$ -solutions of convection-diffusion equations, Nonlinear Diffusion Seminar, UAM, Madrid, Spain. Spring 2019 (February 12): Nonlocal (and local) nonlinear diffusion equations. Background, analysis, and numerical approximation, Scientific Seminar, BCAM, Bilbao, Spain. Fall 2018 (November 21): Numerical solutions of nonlocal (and local) equations of porous medium type, NTNU Workshop on PDEs, Workshop, Trondheim, Norway. Fall 2018 (September 27): Life as a PhD candidate, Introduction seminar for PhD candidates at NTNU, Trondheim, Norway. Spring 2018 (May 25): On nonlocal (and local) equations of porous medium type, Nonlocal Interactions in Partial Differential Equations and Geometry, Summer School, Institut Mittag-Leffler, Stockholm, Sweden. Fall 2017 (September 26): Life as a PhD candidate, Introduction seminar for PhD candidates at NTNU, Trondheim, Norway. Fall 2017 (September 1): What is a solution of a PDE? Current concepts used in research beyond classical solutions, why are they needed, how are they related, Trial lecture, Trondheim, Norway. Spring 2017 (May 22–May 26): On nonlocal equations of porous medium type, International Conference on Elliptic and Parabolic Problems, Conference, Gaeta, Italy. Spring 2017 (May 03): On nonlocal equations of porous medium type. Survey of 4 papers, DNA seminar at NTNU, Trondheim, Norway. Fall 2016 (December 13): Local and nonlocal diffusion (Brownian motion and Lévy flights), Informal seminar at Institut Mittag-Leffler, Stockholm, Sweden. Summer 2016 (June 27–July 01): L1 Contraction for Bounded (Nonintegrable) Solutions of Degenerate Parabolic Equations, 3rd Conference on Nonlocal Operators and Partial Differential Equations, Conference, Bedlewo, Poland. Fall 2015 (December 10): On the duality between Hamilton-Jacobi-Bellmann and convection-diffusion equations, A Nonlocal PDEs Day, Workshop, Madrid, Spain. Spring 2015 (March 12): L1 Contraction for Bounded (Nonintegrable) Solutions of Degenerate Parabolic Equations, DNA seminar at NTNU, Trondheim, Norway. Spring 2014 (March 12): Walking randomly in the realm of partial differential equations and probability theory (The Laplace operator and Brownian motion), Student seminar at NTNU, Trondheim, Norway.
	Conferences & Workshops To top	Summer 2023 (June 26–27): Workshop on PDEs, Bucharest, Romania. Summer 2023 (June 13–16): Abelsymposium, Orkanger, Norway. Click to see 2014–2022: Fall 2022 (September 28–30): Waves and Nonlinear Phenomena, Workshop, Trondheim, Norway. Summer 2022 (June 8–10): 2nd Norwegian meeting on PDEs, Conference, Bergen, Norway. Conference picture Spring 2022 (January 17–21): Congreso Bienal de la Real Sociedad Matemática Española (RSME 2022), Conference, Ciudad Real, Spain. Fall 2021 (September 6–10): New Trends in Nonlinear Diffusion: a Bridge between PDEs, Analysis and Geometry (Online), Virtual workshop. Fall 2020–Spring 2021: Fifty Years of Kruzhkov Entropy Solutions, and Beyond, Thematic online trimester. Fall 2020 (December 11–12): Online Workshop on Nonlocal PDEs, Virtual workshop. Fall 2020 (October 26–30): Nonlocal Operators and Markov Processes I, Virtual workshop. Fall 2020 (October 19–23): 2020 Fields Medal Symposium, Virtual conference. Summer 2020 (June 8–12): Intensive week on PDEs, Virtual workshop. Spring 2020 (February 24): 2nd IMI one-day workshop on PDEs, Workshop, Madrid, Spain. Spring 2020 (January 27–31): V Congreso de Jovénes Investigadores Castelló 2020 (JOVENESRSME 2020), Conference, Castelló, Spain. Conference picture Spring 2019 (June 18–21): The Mathematics of Finite Elements and Applications 2019 (MAFELAP 2019), Conference, London, UK. Spring 2019 (June 5–7): Norwegian meeting on PDEs, Conference, Trondheim, Norway. Spring 2019 (February 4–8): Congreso Bienal de la Real Sociedad Matemática Española (RSME 2019), Conference, Santander, Spain. Spring 2019 (January 18): IMI one-day workshop on PDEs, Workshop, Madrid, Spain. Fall 2018 (November 21–November 23): NTNU Workshop on PDEs, Workshop, Trondheim, Norway. Fall 2018 (September 17–September 20): UMI-SIMAI-PTM Joint Meeting, Conference, Wrocław, Poland. Spring 2018 (May 21–May 25): Nonlocal Interactions in Partial Differential Equations and Geometry, Summer School, Institut Mittag-Leffler, Stockholm, Sweden. Conference picture Summer 2017 (June 26–June 30): The Fractional Laplacian: Probabilistic Structure and Extensions Related to Lévy Processes, Minischool (presented by Krzysztof Bogdan), Bilbao, Spain. Spring 2017 (May 22–May 26): International Conference on Elliptic and Parabolic Problems, Conference, Gaeta, Italy. Spring 2017 (March 22–March 29): Minischool on Recent Trends in PDEs, Minischool (presented by Moritz Kassmann and Juan Luis Vázquez), Madrid, Spain. Fall 2016 (September 22–September 23): Math Meets Industry, Conference, Trondheim, Norway. Summer 2016 (July 04–July 07): Non-linear PDEs, mathematical physics, and stochastic analysis, Conference, Trondheim, Norway. Conference picture Summer 2016 (June 27–July 01): 3rd Conference on Nonlocal Operators and Partial Differential Equations, Conference, Bedlewo, Poland. Conference picture Fall 2015 (December 10): A Nonlocal PDEs Day, Workshop, Madrid, Spain. Spring 2015 (April 27–30): 5. École de printemps EDP Non-linéaire, Conference, Essaouira, Morocco. Summer 2014 (June 19–20): Journées d’Analyse Non Linéaire de Besançon, Workshop, Besançon, France.
	Organized events To top	Spring 2023 (May 24–26): Workshop on nonlocal and nonlinear PDEs, Trondheim, Norway. Conference picture Spring 2023 (May 11–12): Diffusions in Warsaw, Warsaw, Poland. Summer 2022 (June 13–17): Regularity for nonlinear diffusion equations. Green functions and functional inequalities, Madrid, Spain.
	Teaching To top	Spring 2024: No teaching. Click to see previous teaching: Fall 2023: Coordinator/Lecturer TMA4100 (Calculus 1). Spring 2023: Lecturer MA1103 (Vector Calculus). Fall 2022: Lecturer TMA4100 (Calculus 1). Spring 2020: Lecturer TMA4105 (Calculus 2). Fall 2019: Lecturer TMA4100 (Calculus 1). Fall 2018: Lecturer TMA4100 (Calculus 1). Spring 2018: Lecturer TMA4105 (Calculus 2). Summer 2015: Lecturer Oppfriskningskurs matematikk. Spring 2015: Teaching assistant TMA4105. Fall 2014: Teaching assistant TMA4100. Summer 2014: Lecturer Oppfriskningskurs matematikk. Spring 2014: Teaching assistant TMA4105. Fall 2013: Teaching assistant TMA4100.
	For students To top	Bachelor-, prosjekt- og masteroppgaver Click to see previous students: Sander Evensen, Well-posedness for the heat equation, Specialization Project, 2023. Ida Marie Sandum, Solutions to Lotka-Volterra Models Using Numerical Analysis and Simulations, Specialization Project, 2023.
	Miscellaneous To top	Notes on different solution concepts for scalar conservation laws. (Disclaimer: Contains known and unknown errors.) Appearance in local newspaper.

Photo © Emil Sollie / Red Bull Content Pool (2016)

Photo © Fernando Quirós (2023)

Updated April 2024

Copyright © Jørgen Endal 2024

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