Team 5 Study of systems governed by differential equations

In various fields of physics and engineering sciences, the phenomena encountered are modeled by equations or systems of time-dependent differential equations, linear or non-linear, supplemented by initial conditions and boundary conditions of different types. (Dirichlet, Neumann, Robin, integrals, etc.). The mathematical analysis and numerical treatment of these problems constitutes the key to understanding and controlling these phenomena. To this end, the main axes around which our research is structured are: Theoretical analysis (existence, uniqueness and explosion in finite time of solutions) for a class of linear and non-linear parabolic equations with local and non-classical conditions. local (integrals).
Also, among the main goals of this topic is improved and developed the previous study of boundary problems for a class of linear and nonlinear parabolic equations with nonlocal conditions in a Sobolev functional space, as well as for a condition integral of the first and second type, the type of a nonlocal condition depends on the presence or absence of a term containing a trace of the required solution or its derivative outside the integral.
The method that will be used is the Faedo-Galerkin method for the problems of nonlinear parabolic equations with integral condition or non-local in the general sense.
Afterwards ; we study the explosion in finite time solution for a super-linear or semi-linear problem with an integral condition of the 2nd type where the Neumann or Dirichlet condition is equal to an integral condition with weight.
Finally, we move on to the numerical study using different methods of numerical analysis which we adapt to resolve the problems raised.

Running as of 31/12/2018