All Stories

  1. New mathematical issues in models of biological phenomenon of chemotaxis

    Article • Annales Mathematicae Silesianae, September 2018, De Gruyter

    Piotr Biler

  2. Blowing up radial solutions in the minimal Keller–Segel model of chemotaxis

    Article • Journal of Evolution Equations, September 2018, Springer Science + Business Media

    Piotr Biler

  3. Large global-in-time solutions to a nonlocal model of chemotaxis

    Article • Advances in Mathematics, May 2018, Elsevier

    Piotr Biler

  4. Mathematical problems

    Article • October 2017, Taylor & Francis

    Piotr Biler

  5. Local criteria for blowup in two-dimensional chemotaxis models

    Article • Discrete and Continuous Dynamical Systems, December 2016, American Institute of Mathematical Sciences (AIMS)

    Piotr Biler

  6. Morrey spaces norms and criteria for blowup in chemotaxis models

    Article • Networks & Heterogeneous Media, March 2016, American Institute of Mathematical Sciences (AIMS)

    Piotr Biler

  7. Optimal criteria for blowup of radial andN-symmetric solutions of chemotaxis systems

    Article • Nonlinearity, November 2015, Institute of Physics Publishing

    Piotr Biler

  8. Large global-in-time solutions of the parabolic-parabolic Keller-Segel system on the plane

    Article • Communications on Pure & Applied Analysis, September 2015, American Institute of Mathematical Sciences (AIMS)

    Piotr Biler

  9. The Nonlocal Porous Medium Equation: Barenblatt Profiles and Other Weak Solutions

    Article • Archive for Rational Mechanics and Analysis, August 2014, Springer Science + Business Media

    Piotr Biler

  10. Blowup in higher dimensional two species chemotactic systems

    Article • Communications on Pure & Applied Analysis, September 2012, American Institute of Mathematical Sciences (AIMS)

    Piotr Biler

  11. Blowup and self-similar solutions for two-component drift–diffusion systems

    Article • Nonlinear Analysis, September 2012, Elsevier

    Piotr Biler

  12. Barenblatt profiles for a nonlocal porous medium equation

    Article • Comptes Rendus Mathématique, June 2011, Elsevier

    Piotr Biler

  13. An elementary approach to nonexistence of solutions of linear parabolic equations

    Article • Colloquium Mathematicum, January 2011, Institute of Mathematics, Polish Academy of Sciences

    Piotr Biler

  14. Large mass self-similar solutions of the parabolic–parabolic Keller–Segel model of chemotaxis

    Article • Journal of Mathematical Biology, August 2010, Springer Science + Business Media

    Piotr Biler, Jean Dolbeault

  15. Blowup of solutions to generalized Keller–Segel model

    Article • Journal of Evolution Equations, November 2009, Springer Science + Business Media

    Piotr Biler

  16. Nonlinear Diffusion of Dislocation Density and Self-Similar Solutions

    Article • Communications in Mathematical Physics, June 2009, Springer Science + Business Media

    Piotr Biler

  17. Blowup of solutions to a diffusive aggregation model

    Article • Nonlinearity, May 2009, Institute of Physics Publishing

    Piotr Biler

  18. Two-dimensional chemotaxis models with fractional diffusion

    Article • Mathematical Methods in the Applied Sciences, January 2009, Wiley

    Piotr Biler

  19. On the parabolic-elliptic limit of the doubly parabolic Keller–Segel system modelling chemotaxis

    Article • Studia Mathematica, January 2009, Institute of Mathematics, Polish Academy of Sciences

    Piotr Biler

  20. Nonexistence of solutions of the heat diffusion problem on a punctured disc

    Article • Monatshefte für Mathematik, November 2008, Springer Science + Business Media

    Piotr Biler

  21. General nonlocal diffusion–convection mean field models: Nonexistence of global solutions

    Article • Physica A Statistical Mechanics and its Applications, June 2007, Elsevier

    Piotr Biler

  22. Global existence versus blow up for some models of interacting particles

    Article • Colloquium Mathematicum, January 2006, Institute of Mathematics, Polish Academy of Sciences

    Piotr Biler

  23. The 8π-problem for radially symmetric solutions of a chemotaxis model in the plane

    Article • Mathematical Methods in the Applied Sciences, January 2006, Wiley

    Piotr Biler

  24. Global regular and singular solutions for a model of gravitating particles

    Article • Mathematische Annalen, July 2004, Springer Science + Business Media

    Piotr Biler

  25. Asymptotic properties of solutions of the viscous Hamilton-Jacobi equation

    Article • Journal of Evolution Equations, March 2004, Springer Science + Business Media

    Piotr Biler

  26. Global and exploding solutions in a model of self-gravitating systems

    Article • Reports on Mathematical Physics, October 2003, Elsevier

    Piotr Biler

  27. Intermediate asymptotics in L1 for general nonlinear diffusion equations

    Article • Applied Mathematics Letters, January 2002, Elsevier

    Piotr Biler

  28. Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws

    Article • Annales de l Institut Henri Poincaré C Analyse Non Linéaire, September 2001, Elsevier

    Piotr Biler

  29. LARGE TIME ASYMPTOTICS OF NONLINEAR DRIFT-DIFFUSION SYSTEMS WITH POISSON COUPLING

    Article • Transport Theory and Statistical Physics, August 2001, Taylor & Francis

    Piotr Biler

  30. Asymptotics for conservation laws involving Lévy diffusion generators

    Article • Studia Mathematica, January 2001, Institute of Mathematics, Polish Academy of Sciences

    Piotr Biler

  31. Long Time Behavior of Solutions to Nernst-Planck and Debye-Hückel Drift-Diffusion Systems

    Article • Annales Henri Poincaré, July 2000, Springer Science + Business Media

    Piotr Biler

  32. Multifractal and Lévy conservation laws

    Article • Comptes Rendus de l Académie des Sciences - Series I - Mathematics, March 2000, Elsevier

    Piotr Biler

  33. Self-interaction of Brownian particles coupled with thermodynamic processes

    Article • Reports on Mathematical Physics, December 1998, Elsevier

    Piotr Biler

  34. Fractal Burgers Equations

    Article • Journal of Differential Equations, September 1998, Elsevier

    Piotr Biler

  35. Global and Exploding Solutions for Nonlocal Quadratic Evolution Problems

    Article • SIAM Journal on Applied Mathematics, January 1998, Society for Industrial & Applied Mathematics (SIAM)

    Piotr Biler

  36. Nonlocal parabolic problems in statistical mechanics

    Article • Nonlinear Analysis, December 1997, Elsevier

    Piotr Biler

  37. A Singular Problem in Electrolytes Theory

    Article • Mathematical Methods in the Applied Sciences, June 1997, Wiley

    Piotr Biler

  38. Exact estimates for the solutions to a class of homogeneous second order evolution equations

    Article • Applicable Analysis, November 1994, Taylor & Francis

    Piotr Biler

  39. The Debye system: existence and large time behavior of solutions

    Article • Nonlinear Analysis, November 1994, Elsevier

    Piotr Biler

  40. Existence and asymptotics of solutions for a parabolic-elliptic system with nonlinear no-flux boundary conditions

    Article • Nonlinear Analysis, December 1992, Elsevier

    Piotr Biler

  41. Scattering of small solutions to generalized benjamin-bona-mahony equation in several space dimensions

    Article • Communications in Partial Differential Equations, January 1992, Taylor & Francis

    Piotr Biler

  42. Time decay of solutions of semilinear strongly damped generalized wave equations

    Article • Mathematical Methods in the Applied Sciences, August 1991, Wiley

    Piotr Biler

  43. Partition of energy in strongly damped generalized wave equations

    Article • Mathematical Methods in the Applied Sciences, February 1990, Wiley

    Piotr Biler

  44. Perturbed hyperbolic equations

    Article • Proceedings of the Royal Society of Edinburgh Section A Mathematics, January 1989, Cambridge University Press

    Piotr Biler

  45. Regular decay of solutions of strongly damped nonlinear hyperbolic equations

    Article • Applicable Analysis, January 1989, Taylor & Francis

    Piotr Biler

  46. Exponential decay of solutions of damped nonlinear hyperbolic equations

    Article • Nonlinear Analysis, January 1987, Elsevier

    Piotr Biler

  47. Remark on the decay for damped string and beam equations

    Article • Nonlinear Analysis, January 1986, Elsevier

    Piotr Biler

  48. Stochastic interpretation of potential scattering in quantum mechanics

    Article • Letters in Mathematical Physics, January 1984, Springer Science + Business Media

    Piotr Biler