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PDE models of controlled growth
PDE and Applied Math Seminar| Speaker: | Alberto Bressan, Penn State Univ. |
| Related Webpage: | https://www.math.psu.edu/bressan/ |
| Location: | 3106 MSB |
| Start time: | Fri, Jun 2 2017, 11:00AM |
Living tissues, such as stems, leaves and flowers in plants, or bones in animals, grow into a great variety of shapes. In some cases, Nature has found ways to control this growth with remarkable accuracy.
In this talk I shall discuss some free boundary problems modeling controlled growth, namely:
(I) Growth of 1-dimensional curves in R^3 (tree stems, vines), where the shape is determined by a feedback response to gravity and to external obstacles.
(II) Growth of 2 or 3-dimensional domains, controlled by the concentration of a morphogen, coupled with the minimization of an elastic deformation energy.
Some recent existence, uniqueness, and stability results will be presented, together with numerical simulations. Further directions will be discussed.
Special time and room.