Seminar in PDE and Applications
The idea of this seminar is to bring together local and international experts in the field of partial differential equations (PDE) and related fields. In the talks we want to cover various aspects of PDE and their applications, including modeling, mathematical analysis and numerics. Our goal is to increase the visibility of work that is being done in the field of PDE across the different groups at DIAM and to serve as a meeting platform within the department.
The seminar takes place on Thursdays at 4pm.
If you are interested in talks about topics in Applied Analysis, check out the seminar page.
Yves van Gennip (MP)
Anna Geyer (MP)
Manuel Gnann (AA)
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06 April 2023 16:00 till 17:00
[PDE & Applications seminar] Johan Dubbeldam: Using mathematical modeling and game theory to optimize therapy in cancer patientsIn this talk I will present a game-theoretic model of a cancer cell population where the treatment-induced resistance is a quantitative evolving trait and the sensitive and resistant cancer cells compete with each other. We first investigate whether a constant treatment dose can stabilize the tumor burden at an acceptable level. When stabilization is possible, we expand the model into a Stackelberg evolutionary game (SEG), with the physician as the leader and the cancer cells as followers. Here the physician chooses a treatment dose to maximize the patient's quality of life, while the cancer cells evolve resistance to the treatment in order to better proliferate and survive. We find the Nash and Stackelberg equilibria of the SEG game, corresponding to the ecological (or ecologically enlightened) therapy and evolutionary (or evolutionarily enlightened) therapy, respectively, and compare them to the outcomes of applying the maximum tolerable dose (MTD). Finally, some recent work about applying control theory to these models will be discussed. This work was done in collaboration with Hasti Garjani, Frederik Thomsen and Katerina Stankova, Monica Salvioli
20 April 2023 16:00 till 17:00
[PDE & Applications seminar] Zivorad Tomovski: Fractional Poisson process and ApplicationsThe name fractional Poisson process is due to Laskin 2003 who
one point counting distribution. The renewal process of Mittag Leffler
type was discussed by Gorenflo, Mainardi and Scalas in two papers
published in 2004 one of them specifically devoted to the process and
on the Vietnam Journal of Mathematics. Hilfer and Anton 1995 were the first
to recognize the relation between the Mittag Leffler function and the time
fractional diffusion equation. The use of the Mittag Leffler function in
framework can be traced back to works of Gnedenko and Kovalenko 1968 on
thinning and Balakrishnan 1985 on anomalous diffusion. We will discuss
Poisson process by considering Hilfer-Prabhakar derivative in
difference-differential equations governing the dynamics of generalized
renewal stochastic processes.