On March 12–26, 2024, researches of MCA project “Differential Equations and Dynamic Systems”, Doctor of Physical and Mathematical Sciences, Professor Gennady V. Demidenko and Doctor of Physical and Mathematical Sciences, Associate Professor Inessa I. Matveeva, at the invitation of colleagues from China, were with working visit to Shanghai (China). They gave a series of lectures for undergraduate and graduate students at Shanghai University, held scientific seminars, and discussed the development of joint scientific research and holding conferences with colleagues from China.
A series of lectures by Gennady Demidenko was devoted to partial differential equations that were not resolved with respect to the highest derivative. A classification of equations is given and special scales of weighted Sobolev spaces are introduced. Theorems on the solvability of the Cauchy problem and mixed boundary value problems for such equations are proved.
A series of lectures by Inessa Matveeva was devoted to the stability of solutions to non-autonomous equations with delay. Stability conditions were specified using special classes of Lyapunov–Krasovsky functionals. Estimates are established that characterize the rate of decay of solutions at infinity and estimates for attraction sets.
During the visit, a discussion was held on the organization and holding of the Chinese-Russian Conference on Differential Equations, which will take place on August 2–4, 2024 in Dalian (China) with the support of the Mathematical Center in Academgorodok. G. V. Demidenko is the co-chairman of this conference from the Russian side, I. I. Matveeva — member of the international program committee. This conference is a continuation of the Russian-Chinese Conference on Differential Equations, which took place on November 2–6, 2023 in Novosibirsk and was organized by members of the group “Differential equations and dynamical systems” with the support of the Mathematical Center in Akademgorodok.
