[專題演講] 【03月29日】Van Tien Nguyen / Singularity formation in Nonlinear Parabolic Problems

Singularity formation in Nonlinear Parabolic Problems

時 間:2023-03-29 14:00 (星期三) / 地 點:M212 / 茶 會:M107 (13:30)

Van Tien Nguyen (阮文先)
Department of Mathematics, National Taiwan University

Many central problems in geometry, mathematical physics and biology reduce to questions regarding the behavior of solutions of nonlinear evolution equations. The global dynamical behavior of bounded solutions for large times is of signi cant interest. However, in many real situations, solutions develop singularities in nite time. The singularities have to be analyzed in details before attempting to extend solutions beyond their singularities or to understand their geometry in conjunction with globally bounded solutions. In this context we have been particularly interested in qualitative descriptions of blowup. Particular examples include semilinear reaction-di usion systems, harmonic map heat ows, and the classical Keller-Segel system of modeling chemotaxis. I will present constructive approaches based on spectral analysis and energy-type estimates for the question of existence of blowup solutions to these particular models.

友善列印

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