Joint analytical and numerical investigation of blow-up in some mathematical models

Speaker

Dr Alexander Panin (Lomonosov MSU, faculty of physics, chair of mathematics)

Description

In some models (for example, in plasma physics and semiconductor physics), the blow-up phenomenon occurs, i. e. the solution's norm tends to infinity as time tends to a finite moment. There exist some methods to detect blow-up analytically: Pokhozhaev and Mitidieri's test function method, Levine's method, and Samarskii and Galaktionov's similarity solutions method. These methods typically provide us with an estimation of the blow-up moment. The numerical algorithm (based on N. N. Kalitkin and co-authors' ideas), however, allows us to specify the moment and the process of the solution’s blow-up by using Richardson's effective accuracy order. In particular, one can obtain the blow-up moment with the accuracy up to mesh interval. Some numerical experiments will be presented in order to demonstrate the effectiveness of the method.

Short biography note

  1. A.B. Al’shin, E.A. Al’shina, Numerical diagnosis of blow-up of solutions of pseudoparabolic equations, J. Math. Sci. 148(1) (2008), 143–162.
  2. N.N. Kalitkin, A.B. Al’shin, E.A. Al’shina, B.V. Rogov, Computations on Quasi-uniform Grids, Fizmatlit, Moscow, 2005 (in Russian).
  3. Korpusov M.O., Lukyanenko D.V., Panin A.A., Yushkov E.V. Blow-up for one Sobolev problem: theoretical approach and numerical analysis. JMAA, 442(2) (2016), 451-468.

Primary author

Dr Alexander Panin (Lomonosov MSU, faculty of physics, chair of mathematics)

Co-authors

Dr Dmitry Lukyanenko (Lomonosov MSU, faculty of physics, chair of mathematics) Prof. Maxim Korpusov (Lomonosov MSU, faculty of physics, chair of mathematics)

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