| Abstract: |
| The presentation will cover results concerning linear non-autonomous systems of parabolic partial differential equations with delay. More specifically, I will present theorems regarding the existence and uniqueness of such initial-boundary value problems. Additionally, I will discuss theorems on the regularization of solutions over time and the continuous dependence of solutions on parameters (not just the initial condition) among other functional coefficients of the equation.
These types of equations are important for many reasons; however, it should be noted that they generate dynamical systems, and their random versions generate measurable skew-product semi-flows for which the theory of Lyapunov exponents, exponential separation, and Oseledets decomposition is still being developed. Moreover, models based on this type of differential equations are important in mathematical ecology, particularly when modeling interactions between species.
The presentation will be based on joint work with Janusz Mierczy\`{n}ski. |
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