Collaborative research on nonlinear PDEs and integro-differential equations
The proposal develops and applies new constructive methods in the study of solutions of nonlinear partial differential equations, with focus on existence and uniqueness, regularity and spontaneous formation of singularities. Recent advances in Borel-Laplace regularization and summability are used to find global properties of solutions of PDEs. There is a wide range of problems where these questions are essential, and a number of concrete examples including thin film equations, Kuramoto-Sivashinski, KdV and mKdV will be analyzed.
Natural phenomena in physics, chemistry, material sciences and in many other disciplines are most often described by differential equations; complex phenomena are frequently modeled by partial differential equations. The present project covers a wide range of such equations, the global properties of their solutions and their possible blow up. This resarch is a piece of an unfolding enterprise to advance a theory of singular behavior, of substantial importance in mathematics and its applications.
