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Abstract:
Understanding the asymptotic behavior of solutions to stationary and time dependent nonlinear PDEs is crucial for the analysis of the existence and qualitative properties of the solutions such as regularity, symmetry, stability, front propagation. It is also fundamental for the apriori nonexistence results such as Liouville type theorems in elliptic and finite time blowup in parabolic problems. The aim of this special session is to bring together leading experts on linear and nonlinear PDEs for the exchange of ideas and most recent advances in these areas. Relevant topics from the linear theory will include Green`s functions and heat kernels estimates; maximum principles and regularity theory; involving probabilistic methods. The focus in nonlinear PDEs will be on elliptic and parabolic problems including equations on manifolds and problems with nonlocal interactions, as well as travelling waves solutions.
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