Invitaţie: În data de 20 martie 2025 (joi), între orele 10:30-11:30, în sala e,  vă invităm la prezentarea susținută de Prof. univ. dr. Erika Hausenblas (Montanuniversität Leoben, Austria), având titlul Cross-diffusion systems with random perturbation.

Abstract: Cross-diffusion is a phenomenon that occurs in various applications, e.g. in population dynamics, ecology, biology, or material science. Cross-diffusion describes systems with multiple components or different species, where the concentration gradient of one component influences the motion of another component. In other words, cross-diffusion occurs if the diffusion of one substance is affected by the presence of another substance.

These cross-coupling terms can lead to complex and often nonlinear behaviour, such as pattern formation or spatial segregation of different components and blow-up phenomena.

Cross-diffusion is commonly observed in many physical, chemical, and biological systems, including chemical reactions, population dynamics, and fluid dynamics. It plays an essential role in many natural and technological processes, such as the spread of pollutants in the environment, the formation of biological patterns, and the design of advanced materials with tailored properties.

The most important cross-diffusion systems are the Shigesada-Kawasaki-Teramoto model from population dynamics, the Maxwell-Stefan system in material science, and chemotaxis in biochemistry.

We will consider in the talk a certain system of cross-diffusion, i.e. chemotaxis, and proof of existence and uniqueness of the solution by a fix point Theorem.

https://angemath.unileoben.ac.at/en/team/erika-hausenblas