Research output per year
Research output per year
Personal profile
Research Interests
The backbone of my research is the mathematical modelling of various nonlinear processes with evolution equations or strongly coupled systems thereof and their qualitative study.
Examples include: degenerate/singular diffusion, chemo-/haptotaxis, adhesion, growth, and stochastic perturbations.
The analysis involves well-posedness, regularity, long-time behaviour, as well as other qualitative properties. Main applications are concerned with the mathematical modelling for life sciences.
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Collaborations and top research areas from the last five years
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Global existence of solutions to a nonlocal equation with degenerate anisotropic diffusion
Eckardt, M. & Zhigun, A., 15 Mar 2025, In: Journal of Mathematical Analysis and Applications. 543, Issue 2, Part 2, 22 p., 128971.Research output: Contribution to journal › Article › peer-review
Open AccessFile2 Citations (Scopus)8 Downloads (Pure) -
Local well-posedness for a novel nonlocal model for cell-cell adhesion via receptor binding
Rajendran, M. L. & Zhigun, A., 31 Aug 2025, In: SIAM Journal on Mathematical Analysis. 57, 4, p. 4016 - 4067Research output: Contribution to journal › Article › peer-review
Open AccessFile10 Downloads (Pure) -
Global entropy solutions to a degenerate parabolic-parabolic chemotaxis system for flux-limited dispersal
Zhigun, A., Oct 2024, In: Nonlinear Analysis: Real World Applications. 79, 34 p., 104132.Research output: Contribution to journal › Article › peer-review
Open AccessFile1 Citation (Scopus)75 Downloads (Pure) -
Modelling non-local cell-cell adhesion: a multiscale approach
Zhigun, A. & Rajendran, M. L., May 2024, In: Journal of Mathematical Biology. 88, 5, 35 p., 55.Research output: Contribution to journal › Article › peer-review
Open AccessFile4 Citations (Scopus)38 Downloads (Pure) -
A novel derivation of rigorous macroscopic limits from a micro-meso description of signal-triggered cell migration in fibrous environments
Zhigun, A. & Surulescu, C., 13 Jan 2022, In: SIAM Journal on Applied Mathematics. 82, 1Research output: Contribution to journal › Article › peer-review
Open AccessFile8 Citations (Scopus)128 Downloads (Pure)
Activities
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On some highly nonlinear parabolic systems for cell migration
Zhigun, A. (Invited speaker)
11 Nov 2022Activity: Talk or presentation types › Invited talk
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12th European Conference on Mathematical and Theoretical Biology
Zhigun, A. (Organiser)
19 Sept 2022Activity: Participating in or organising an event types › Participation in workshop, seminar, course
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Workshop on free boundary problems in biology and fluid dynamics
Zhigun, A. (Invited speaker)
13 Sept 2022Activity: Participating in or organising an event types › Participation in workshop, seminar, course
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Oberwolfach Seminar on Taxis-Type Evolution Systems: Modeling and Analysis
Zhigun, A. (Organiser)
05 Jun 2022 → 11 Jun 2022Activity: Participating in or organising an event types › Participation in workshop, seminar, course