| Abstract: |
| The well-posedness in the sense of Hadamard for systems of PDEs and ODEs is investigated. Particularly, we are interested in reaction-diffusion equations and systems in bounded domains with delays in reaction terms. Different types of solutions (different phase spaces) are discussed. A recent study of viral in-host infection models with state-dependent delay is also described. It includes PDE and/or ODE infection models with /without CTL and antibody immune responses. A delay in such systems is a natural parameter (functional of the state) describing the biological delay between the time a virus particle contacts a target cell and the time the cell becomes actively infected (start producing new virions). |
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