Prof. dr hab. Piotr Gwiazda

List of publications

Peer reviewed journals

  1. Conservation of energy for the Euler-Korteweg equations (with Tomasz Dębiec, Agnieszka Świerczewska-Gwiazda and Anthanasios Tzavaras), arXiv:1801.00177 accepted Calc. Var. Partial Differential Equations
  2. On the Extension of Onsager's Conjecture for General Conservation Laws (join work with Claude Bardos, Agnieszka Świerczewska-Gwiazda, Edriss S. Titi, Emil Wiedemann) arXiv:1806.02483 accepted Journal of Nonlinear Sciences
  3. Relative Entropy Method for Measure Solutions of the Growth-Fragmentation Equation (joint work with Tomasz Dębiec, Marie Doumic, Piotr Gwiazda, Emil Wiedemann) arXiv:1804.03538 accepted SIAM J. Math. Anal.
  4. Well-posedness of parabolic equations in the non-reflexive and anisotropic Musielak-Orlicz spaces in the class of renormalized solutions (joint work with Iwona Skrzypczak, Anna Zatorska-Goldstein) arXiv:1707.06097 accepted J. Differential Equations
  5. Gossez's approximation theorems in the Musielak-Orlicz-Sobolev spaces (joint work with Youssef Ahmida, Iwona Skrzypczak, Ahmed Youssfi) arXiv:1711.06145 accepted J. Funct. Anal. https://doi.org/10.1016/j.jfa.2018.05.015
  6. Existence of global weak solutions to the kinetic Peterlin model (join work with Mária Lukáčová-Medviďová, Hana Mizerová, Agnieszka Świerczewska-Gwiazda) arXiv:1707.02783 accepted Nonlinear Anal. Real World Appl.
  7. A note on weak solutions of conservation laws and energy/entropy conservation (joint work with Martin Michálek, Agnieszka Świerczewska-Gwiazda), arXiv:1706.10154 accepted Arch. Ration. Mech. Anal. https://doi.org/10.1007/s00205-018-1238-0
  8. Measures under the flat norm as ordered normed vector space. (joint work with Marciniak-Czochra, Anna; Thieme, Horst R.) Positivity 22 (2018), no. 1, 105–138. DOI 10.1007/s11117-017-0503-z
  9. Existence of renormalized solutions to elliptic equation in Musielak-Orlicz space, (joint work with Iwona Skrzypczak, Anna Zatorska-Goldstein)  J. Differential Equations 264 (2018), no. 1, 341–377. arXiv:1701.08970
  10. Thermo-visco-elasticity for Norton-Hoff-type models with homogeneous thermal expansion, (with Filip Klawe, Sebastian Owczarek)  Nonlinear Anal. Real World Appl. 40 (2018), 337–360. arXiv:1611.05188
  11. Optimization in Structure Population Models through the Escalator Boxcar Train (with Rinaldo M. Colombo and Magdalena Rosinska) to appear ESAIM: Control, Optimisation and Calculus of Variations, DOI: https://doi.org/10.1051/cocv/2017003, arXiv:1601:07870
  12. Weak solutions for Euler systems with non-local interactions, (with J.A. Carrillo, E. Feireisl, A. Świerczewska-Gwiazda), J. Lond. Math. Soc. (2) 95 (2017), no. 3, 705–724. arXiv:1512.03116
  13. Regularity and Energy Conservation for the Compressible Euler Equations (with Eduard Feireisl, A. Świerczewska-Gwiazda and Emil Wiedemann),  Arch. Ration. Mech. Anal. 223 (2017), no. 3, 1375–1395. , DOI
    10.1007/s00205-016-1060-5, arXiv:1603.05051
  14. Generalized Entropy Method for the Renewal Equation with Measure Data (with Emil Wiedemann), Commun. Math. Sci. 15 (2017), no. 2, 577–586, arXiv:1604.07657
  15. Finite Range Method of Approximation for Balance Laws in Measure Spaces, (with  Piotr Orlinski and Agnieszka  Ulikowska),  Kinet. Relat. Models 10 (2017), no. 3, 669–688.,  arXiv:1409.0766
  16. On unified theory for scalar conservation laws with fluxes and sources discontinuous with respect to the unknown (joint work with Miroslav Bulicek and Agnieszka Świerczewska–Gwiazda)  J. Differential Equations 262 (2017), no. 1, 313–364, arXiv:1606.06500
  17. Dissipative measure-valued solutions to the compressible Navier-Stokes system (with Eduard Feireisl, A. Świerczewska-Gwiazda and Emil Wiedemann), Calc. Var. Partial Differential Equations 55 (2016), no. 6, 55:141, arXiv:1512.04852
  18. Transport equation with integral terms (with Camillo De Lellis and A. Świerczewska-Gwiazda), Calc. Var. Partial Differential Equations 55 (2016), no. 5, 55:128, arXiv:1602.03193
  19. Age-structured population model of infectious disease spread applied to data on varicella prevalence in Poland (with Blazej Miasojedow and Magdalena Rosinska),  J. Theoret. Biol. 407 (2016), 38–50., arXiv:1602.03193
  20. Analysis of a viscosity model for concentrated polymers, (with Miroslav Bulicek,  Endre Suli and Agnieszka Swierczewska–Gwiazda), Math. Models Methods Appl. Sci. 26 (2016), no. 8, 1599–1648., arXiv:1501.05766
  21. On weak solutions to the 2D Savage-Hutter model of the motion of a gravity driven avalanche flow, (with Eduard Feireisl and Agnieszka Swierczewska–Gwiazda), Comm. Partial Differential Equations 41 (2016), no. 5, 759–773., DOI:10.1080/03605302.2015.1127968, arXiv:1502.06223
  22. Mass concentration in a nonlocal model of clonal selection, (with Busse, Jan-Erik  and Marciniak-Czochra, Anna), J. Math. Biol. 73 (2016), no. 4, 1001–1033. DOI 10.1007/s00285-016-0979-3arXiv:1401.604
  23. Renormalized solutions of nonlinear parabolic problems in generalized Musielak-Orlicz spaces, Nonlinear Anal. 129 (2015), 1–36., (joint work with P. Wittbold, A. Wróblewska and A. Zimmermann)
  24. Weak-Strong Uniqueness for Measure-Valued Solutions of Some Compressible Fluid Models, (joint work with A. Świerczewska–Gwiazda and E. Wiedemann), Nonlinearity 28 (2015), no. 11, 3873–3890., arXiv:1503.05246
  25. Bayesian evidence synthesis to estimate HIV prevalence among MSM in Poland, (with M. Rosińska, A. Presanis, D. De Angelis), Epidemiology and Infection, 2015 Nov 6:1-17
  26. Thermo-visco-elasticity for Norton-Hoff-type models, (joint work with Filip Klawe and Agnieszka Świerczewska–Gwiazda), Nonlinear Anal. Real World Appl. 26 (2015), 199–228., arXiv:1404.1671
  27. Multi-dimensional scalar balance laws with discontinuous flux, (joint work with Agnieszka Świerczewska–Gwiazda, Petra Wittbold and Aleksandra Zimmermann), J. Funct. Anal. 267 (2014), no. 8, 2846–2883., arXiv:1404.2036
  28. Splitting-Particle Methods for Structured Population Models: Convergence and Applications Math. Models Methods Appl. Sci. 24 (2014), no. 11, 2171–2197.  (joint work with J.A. Carrillo and A.Ulikowska)
  29. Analysis of particle methods for structured population models with nonlocal boundary term in the framework of bounded Lipschitz distance, Numer. Methods Partial Differential Equations 30 (2014), no. 6, 1797–1820. (joint work with J. Jablonski, A. Marciniak-Czochra and A.Ulikowska)
  30. Multi-dimensional scalar conservation laws with fluxes discontinuous in the unknown and the spatial variable (joint work with Miroslav Bulicek and Agnieszka Świerczewska–Gwiazda), Math. Models Methods Appl. Sci. 23 (2013), no. 3, 407–439.
  31. On unstedy flows of implicitly constituted incompressible fluids SIAM J. Math. Anal. 44 (2012), no. 4, 2756–2801. (joint work with Miroslav Bulicek, Josef Malek, Agnieszka Swierczewska–Gwiazda)
  32. Models of discrete and continuous cell differentiation in the framework of transport equation (joint work with G.Jamróz, A.Marciniak-Czochra), SIAM J. Math. Anal. 44 (2012), no. 2, 1103–1133. pdf
  33. Elliptic problem in generalized Orlicz-Musielak spaces (joint work with Piotr Minakowski and Aneta Wróblewska),  Central European Journal of Mathematics,    10(6), pp. 2019-2032, (2012) pdf
  34. Renormalized solutions of nonlinear elliptic problems in generalized Orlicz spaces (joint work with Petra. Wittbold, Aneta. Wróblewska and Aleksandra Zimmermann), J. Differential Equations 253 (2012), no. 2, 635–666. pdf
  35. Structured Populations, Cell Growth and Measure Valued Balance Laws (joint work with J.A. Carrillo, R.M. Colombo and A.Ulikowska) J. Differential Equations 252 (2012), no. 4, 3245–3277. pdf
  36. Generalized Stokes system in Orlicz spaces (joint work with Agnieszka Swierczewska–Gwiazda and Aneta Wróblewska), Discrete Contin. Dyn. Syst. 32 (2012), no. 6, 2125–2146. pdf
  37. On scalar hyperbolic laws with discontinuous flux, Math. Models Methods Appl. Sci. 21 (2011), no. 1, 89–113. (joint work with Miroslav Bulicek, Josef Malek, Agnieszka Swierczewska–Gwiazda)
  38. Structured population equations in metric spaces. J. Hyperbolic Differ. Equ. 7 (2010), no. 4, 733–773. (joint work with Anna Marciniak-Czochra)
  39. A nonlinear structured population model: Lipschitz continuity of measure-valued solution with respect to model ingredients. J. Differential Equations 248 (2010), no. 11, 2703–2735. (joint work with Anna Marciniak-Czochra and Thomas Lorentz)
  40. Monotonicity methods in generalized Orlicz spaces for a class of non-Newtonian fluids Math. Methods Appl. Sci. 33 (2010), no. 2, 125–137. (joint work with Agnieszka Swierczewska–Gwiazda, Aneta Wroblewska)
  41. On steady non-Newtonian flows with growth conditions in generalized Orlicz spaces, Topol. Methods Nonlinear Anal. 32 (2008), no. 1, 103–113. (joint work with Agnieszka Swierczewska )
  42. On steady flows of an incompressible fluids with implicit power-law-like rheology, Adv. Calc. Var. 2 (2009), no. 2, 109–136. (joint work with Miroslav Bulicek, Josef Malek, Agnieszka Swierczewska–Gwiazda)
  43. On Non-Newtonian fluids with a property of rapid thickening under different stimulus, Math. Models Methods Appl. Sci. 18 (2008), no. 7, 1073–1092. (joint work with Agnieszka Swierczewska)
  44. Convergence of coercive approximations for strictly monotone quasistatic models in the inelastic deformation theory, Math. Methods Appl. Sci. 30 (2007), no. 12, 1357–1374. (joint work with Krzysztof Chełminski)
  45. On flows of an incompressible fluid with discontinuous power–law–like rheology, Comput. Math. Appl. 53 (2007), no. 3-4, 531–546. (joint work with Josef Malek and Agnieszka Swierczewska) 
  46. On elliptic and parabolic systems with x–dependent multivalued graphs, Math. Methods Appl. Sci. 30 (2007), no. 2, 213–236. (joint work with Anna Zatorska-Goldstein)
  47. Measure valued solutions to conservation laws motivated by traffic modelling. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 462 (2006), no. 2070, 1791–1803. (joint work with Sylvie Benzoni-Gavage, Rinaldo M. Colombo).
  48. Existence via compactness for maximal monotone elliptic operators. C. R. Math. Acad. Sci. Paris 340 (2005), no. 7, 489–492. (joint work with Anna Zatorska-Goldstein)
  49. On measure valued solution to 2–d gravity driven avalanche flow model. Math. Methods Appl. Sci. 28 (2005), no. 18, 2201–2223.
  50. Multivalued equations for granular avalanches. Nonlinear Anal. 62 (2005), no. 5, 895–912. (joint work with Agnieszka Swierczewska)
  51. Large Eddy Simulation turbulence model with Young measures, Appl. Math. Lett. 18 (2005), no. 8, 923–929. (joint work with Agnieszka Swierczewska)
  52. Sensitivity from Constitutive Relations in Materials with Memory, Contin. Mech. Thermodyn. 17 (2005), no. 2, 159–164. (joint work with Rinaldo M. Colombo)
  53. L1 stability of semigroups with respect to their generators, Quart. Appl. Math. 63 (2005), no. 3, 509–526. (joint work with Rinaldo M. Colombo)
  54. An existence result for the Leray-Lions type operators with discontinuous coefficients. Asymptot. Anal. 43 (2005), no. 3, 249–265. (joint work with Anna Zatorska-Goldstein)
  55. An L1 -stability and uniqueness result for balance laws with multifunctions: a model from the theory of granular media. Colloq. Math. 100 (2004), no. 2, 149–162. (joint work with Agnieszka Swierczewska).
  56. An existence result for balance laws with multifunctions: A model from the theory of granular media, Colloq. Math. 97 (2003), no. 1, 67–79.
  57. An existence result for a model of granular material with non-constant density, Asymptot. Anal. 30 (2002), no. 1, 43–60.
  58. On singular limits to Bodner-Partom model. Math. Methods Appl. Sci. 24 (2001), no. 3,
  59. Nonhomogeneous initial-boundary value problems for coercive and self-controlling models of monotone type. Contin. Mech. Thermodyn. 12 (2000), no. 4, 217–234. (joint work with K. Chelminski).
  60. On the model of Bodner-Partom with nonhomogeneous boundary data. Math. Nachr. 214 (2000), 5–23. (joint work with K. Chelminski).
  61. Nonhomogeneous boundary value problem for the Chan-Bodner-Linholm model. Math. Methods Appl. Sci. 23 (2000), no. 11, 1011–1022.
  62. Monotonicity of operators of viscoplastic response: Application to the model of Bodner-Partom. Bull. Pol. Acad. Sci., Tech. Sci. 47, No.3, 191-208 (1999) (joint work with K. Chelminski).
  63. Existence and uniqueness theorem for the Chan-Bodner-Lindholm model. Math. Methods Appl. Sci. 22 (1999), no. 4, 285–300.

Proceedings

  1. Relative entropy method for measure-valued solutions in natural sciences (with Tomasz Dębiec, Agnieszka Świerczewska-Gwiazda and Kamila Łyczek), to appear in Topol. Methods Nonlinear Anal. , arXiv:1709.01410
  2. The Escalator Boxcar Train method for a system of aged-structured equations, Networks and Heterogeneous Media 11 (2016) 123–143, (joint work with Karolina Kropielnicka and Anna Marciniak-Czochra), arXiv:1506.00016
  3. Thermoplasticity for the Mróz's model in the framework of thermodynamically complete systems, Discrete Contin. Dyn. Syst. Ser. S Vol. 7(5), 981-991, 2014 (joint work with Filip Klawe and Agnieszka Świerczewska–Gwiazda)
  4. On flows of fluids described by an implicit constitutive equation characterized by a maximal monotone graph (joint work with Miroslav Bulicek, Josef Malek K.R. Rajagopal and Agnieszka Swierczewska–Gwiazda), Mathematical Aspects of Fluid Mechanics, London Math. Soc. Lecture Note Ser. 402, 23-51, Cambridge Univ. Press, (2012)
  5. On the anisotropic Orlicz spaces applied in the problem of continuum mechanics (joint work with Piotr Minakowski and Agnieszka Swierczewska–Gwiazda), Discrete Contin. Dyn. Syst. Ser. S Vol. 6(5), 1291-1306, (2012)
  6. Parabolic equations in anisotropic Orlicz spaces with general N-functions, special Birkhaeuser volume ”Parabolic Problems. The Herbert Amann Festschrift”, Progress in Nonlinear Differential Equations and Their Applications, Vol. 60, 301–311 (joint work with Agnieszka Swierczewska–Gwiazda)
  7. Turbulent flows of rapidly thickening fluids, Proc. Polish- Japanese Days. GAKUTO, Vol. 32, 2010 (joint work with Agnieszka Swierczewska–Gwiazda and Aneta Wroblewska)
  8. Well-possedness for non-Newtonian flows with general growth conditions, Banach Center Publications 86, 115-128, 2009 (joint work with Agnieszka Swierczewska–Gwiazda, Andrzej Warzynski, Aneta Wroblewska)
  9. Invariants and exponential rate of convergence to steady state in the renewal equation, Markov Processes and Related Fields (special issue) Vol. 12, No. 2, 413–425 (2006) (joint work with Benoit Perthame)
  10. On the model Chan-Bodner-Linholm in the theory of inelastic deformation. Z. Angew. Math. Mech. 81 S3 599-600 (2001).

Preprints

  1. Renormalized solutions to parabolic equations in time and space dependent anisotropic Musielak-Orlicz space in absence of Lavrentiev's phenomenon (join work with Iwona Chlebicka,  Anna Zatorska-Goldstein) arXiv:1807.06464
  2. Parabolic equation in time and space dependent anisotropic Musielak-Orlicz spaces in absence of Lavrentiev's phenomenon (join work with Iwona Chlebicka,  Anna Zatorska-Goldstein) arXiv:1806.06711
  3. The Escalator Boxcar Train Method for a System of Aged-structured Equations in the Space of Measures
    (join work with José A. Carrillo, Karolina Kropielnicka, Anna Marciniak-Czochra) arXiv:1806.01770
  4. Differentiability in perturbation parameter of measure solutions to perturbed transport equation
    (join work with Sander C. Hille, Kamila Łyczek, Agnieszka Świerczewska-Gwiazda) arXiv:1806.00357
     
  5. Dissipative measure valued solutions for general conservation laws (joint work with Ondřej Kreml, Agnieszka Świerczewska-Gwiazda) arXiv:1801.01030
  6.  Existence and homogenization of nonlinear elliptic systems in nonreflexive spaces (join work with
  7. A tribute to conservation of energy for weak solutions (joint work with Tomasz Dębiec, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda) arXiv:1707.09794
  8. Homogenization of nonlinear elliptic systems in nonreflexive Musielak-Orlicz spaces,  (joint work with Miroslav Bulíček, Martin Kalousek, Agnieszka Świerczewska-Gwiazda) arXiv:1703.08355

     
     

 

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