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Non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid

Jianwei Dong, Junhui Zhu, Litao Zhang (2024)

Czechoslovak Mathematical Journal

We study the non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid without viscosity. We first show that the life span of the classical solutions with decay at far fields must be finite for the 1D Cauchy problem if the initial momentum weight is positive. Then, we present several sufficient conditions for the non-existence of global classical solutions to the 1D initial-boundary value problem on $[0, 1]$ . To prove these results, some new average quantities are...

Non-simultaneous blow-up for a reaction-diffusion system with absorption and coupled boundary flux.

Zhou, Jun, Mu, Chunlai (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Note on blow-up of solutions for a porous medium equation with convection and boundary flux

Zhiyong Wang, Jingxue Yin (2012)

Colloquium Mathematicae

De Pablo et al. [Proc. Roy. Soc. Edinburgh Sect. A 138 (2008), 513-530] considered a nonlinear boundary value problem for a porous medium equation with a convection term, and they classified exponents of nonlinearities which lead either to the global-in-time existence of solutions or to a blow-up of solutions. In their analysis they left open the case of a certain critical range of exponents. The purpose of this note is to fill this gap.

Numerical blow-up solutions for some semilinear heat equations.

N'gohisse, Firmin K., Boni, Théodore K. (2008)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Numerical blow-up time for a semilinear parabolic equation with nonlinear boundary conditions.

Assalé, Louis A., Boni, Théodore K., Nabongo, Diabate (2008)

Journal of Applied Mathematics

Numerical investigation of a new class of waves in an open nonlinear heat-conducting medium

Milena Dimova, Stefka Dimova, Daniela Vasileva (2013)

Open Mathematics

The paper contributes to the problem of finding all possible structures and waves, which may arise and preserve themselves in the open nonlinear medium, described by the mathematical model of heat structures. A new class of self-similar blow-up solutions of this model is constructed numerically and their stability is investigated. An effective and reliable numerical approach is developed and implemented for solving the nonlinear elliptic self-similar problem and the parabolic problem. This approach...

Numerical study on the blow-up rate to a quasilinear parabolic equation

Anada, Koichi, Ishiwata, Tetsuya, Ushijima, Takeo (2017)

Proceedings of Equadiff 14

In this paper, we consider the blow-up solutions for a quasilinear parabolic partial differential equation $u_{t} = u^{2} (u_{x x} + u)$ . We numerically investigate the blow-up rates of these solutions by using a numerical method which is recently proposed by the authors [3].