ncku-talk2023-03-08

One Day Workshop at NCKU

DATE 2023-03-08　14:10-15:00

PLACE 數學系館 3F會議室

SPEAKER 阮文先 (Van Tien Nguyen)教授（國立台灣大學數學系）

TITLE Singularity Formation in Nonlinear Parabolic Problems

ABSTRACT Singularity formation and Cauchy Problem for Some Nonlinear PDEs
Organizers: 方永富，史習偉，郭鴻文，關汝琳
Goal: We arrange a series of lectures at introductory level and hope to attract students to appreciate some merits of the PDE topic
Singularity formation in Nonlinear Parabolic Problems Abstract: 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 significant interest. However, in many real situations, solutions develop singularities in finite 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-diffusion systems, harmonic map heat flows, 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.

One Day Workshop at NCKU

DATE	2023-03-08　14:10-15:00

PLACE	數學系館 3F會議室

SPEAKER	阮文先 (Van Tien Nguyen)教授（國立台灣大學數學系）

TITLE	Singularity Formation in Nonlinear Parabolic Problems

ABSTRACT	Singularity formation and Cauchy Problem for Some Nonlinear PDEs Organizers: 方永富，史習偉，郭鴻文，關汝琳 Goal: We arrange a series of lectures at introductory level and hope to attract students to appreciate some merits of the PDE topic Singularity formation in Nonlinear Parabolic Problems Abstract: 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 significant interest. However, in many real situations, solutions develop singularities in finite 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-diffusion systems, harmonic map heat flows, 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.