See full Abstract here

Undoubtedly, reactions diffusion equations model a lot of real-world processes in biology, chemistry, and physics, and global existence of solutions to these equations guarantees the continuity of these processes over long time periods. In this plenary session, we will explain the notion of global existence of solutions to differential equations and present an overview around global existence of some reaction-diffusion systems on the whole space R^n.

See full Abstract here

We consider in this talk an inverse problem in PDE. The problem is to find a parameter  p(x) or a source f(x) in elliptic boundary-value problem:

-\Delta u + p(x)u=f(x) in D\subset R^n (n=2,3)

from the Cauchy's data (u|_\Gamma,(\partial u}/{\partial n}|_\Gamma). This problem is ill-posed. We adopt the following plan.
Examples
Equation of the first kind.
Regularisation of Tikhonov
Numerical examples

See full Abstract here

We prove the existence of solutions for a boundary value problem involving the p-Laplacian, where S is a nested fractal set (we especially consider the Sierpinski Gasket as a specific example) on R^{N-1}$ for N> 3,
S_0 is its boundary, a: S -> R are appropriate functions and alpha, beta and p are reals satisfying an adequate hypothesis.

Keywords: Nested fractals, Sierpinski gasket, Critical point,  p-Laplacian, Variational, Nehari Manifold

See full Abstract here

This talk focuses on a survey and some remarks on inverse and ill-posed problems for anomalous diffusion phenomena. We present new results on regularization methods that have been recently established for backward and generalized elliptic equations, along with unresolved questions in this field.

Keywords: Ill-posed problems, backward problem, time-fractional evolution equations, Generalized elliptic equations, regularization methods.

B. Kaltenbacher, W. Rundell. Inverse Problems for Fractional Partial Differential Equations

See full Abstract here (soon)

Le sujet de cette présentation est l'étude des relations linéaires sur les espaces de Banach réels ou complexes. Les principaux objectifs sont la définition et la caractérisation de différents types de spectres, ainsi que l'extension des notions de spectres considérés pour l'opérateur univalent usuel, borné ou non.

Keywords: (soon)