Séminaires à venir

We explore the existence and uniqueness of a large class of first- and second-order partial differential equations for various regularity assumptions on the coefficients and/or initial data. Starting with regular coefficients on the transport equation to obtain classical solutions, we then progressively lower the regularity assumptions to the minimum, introducing new types of solutions, such as renormalized solutions, to deal with the challenges that arise from this loss of regularity. Finally, we extend these notions to second-order partial differential equations, highlighting the difficulties arising in different settings.