Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

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Nonlinear anomalous diffusion equation. Existence, uniqueness, asymptotics and numerical methods

2015/17/D/ST1/00625

Keywords:

nonlinear diffusion porous medium fractional derivative

Descriptors:

  • ST1_11: Partial differential equations
  • ST1_18: Control theory and optimisation
  • ST1_16: Numerical analysis

Panel:

ST1 - Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution :

Politechnika Wrocławska, Wydział Matematyki

woj. dolnośląskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

dr Łukasz Płociniczak 

Number of co-investigators in the project: 2

Call: SONATA 9 - announced on 2015-03-16

Amount awarded: 152 000 PLN

Project start date (Y-m-d): 2016-03-15

Project end date (Y-m-d): 2018-09-14

Project duration:: 30 months (the same as in the proposal)

Project status: Project settled

Project description

Download the project description in a pdf file

Note - project descriptions were prepared by the authors of the applications themselves and placed in the system in an unchanged form.

Equipment purchased [PL]

  1. Tablet (2 000 PLN)
  2. Komputer przenośny (laptop) (6 000 PLN)

Information in the final report

  • Publication in academic press/journals (7)
  1. Numerical method for Volterra equation with a power-type nonlinearity
    Authors:
    Ł.Płociniczak, H. Okrasińska-Płociniczak
    Academic press:
    Applied Mathematics and Computation (rok: 2018, tom: 337, strony: 452-460), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.amc.2018.05.036 - link to the publication
  2. Compactly supported solution of the time-fractional porous medium equation on the half-line
    Authors:
    Łukasz Płociniczak, Mateusz Świtała
    Academic press:
    Nonlinear Analysis: Real World Applications , Wydawca: Elsevier
    Status:
    Submitted
    DOI:
    brak - link to the publication
  3. Solvability in Holder spaces of an integral equation which models dynamics of the capillary rise
    Authors:
    Hanna Okrasińska-Płociniczak, Łukasz Płociniczak, Juan Rocha, Kishin Sadarangani
    Academic press:
    Journal of Mathematical Analysis and Applications , Wydawca: Elsevier
    Status:
    Submitted
    DOI:
    brak - link to the publication
  4. Numerical schemes for integro-differential equations with Erdelyi-Kober fractional operator
    Authors:
    Łukasz Płociniczak, Szymon Sobieszek
    Academic press:
    Numerical Algorithms (rok: 2017, tom: 76(1), strony: 125-150), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11075-016-0247-z - link to the publication
  5. Existence and uniqueness results for a time-fractional nonlinear diffusion equation
    Authors:
    Łukasz Płociniczak, Mateusz Świtała
    Academic press:
    Journal of Mathematical Analysis and Applications (rok: 2018, tom: 462(2), strony: 1425-1434), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2018.02.050 - link to the publication
  6. Diffusivity identification in a nonlinear time-fractional diffusion equation
    Authors:
    Łukasz Płociniczak
    Academic press:
    Fractional Calculus and Applied Analysis (rok: 2016, tom: 19(4), strony: 843-866), Wydawca: De Gruyter
    Status:
    Published
    DOI:
    10.1515/fca-2016-0046 - link to the publication
  7. Numerical method for a time-fractional porous medium equation
    Authors:
    Łukasz Płociniczak
    Academic press:
    SIAM Journal on Numerical Analysis (rok: 2019, tom: 57(2), strony: 638–656), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/18M1192561 - link to the publication

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