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Volume 22, Issue 2
Existence and Uniqueness of BV Solutions for a Class of Degenerate Boltzmann Equations with Measures as Initial Conditions

Hongjun Yuan & Yan Han

J. Part. Diff. Eq., 22 (2009), pp. 127-152.

Published online: 2009-05

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  • Abstract

The existence and uniqueness of the solutions for the Boltzmann equations with measures as initial value are still an open problem which is posed by P. L. Lions (2000). The aim of this paper is to discuss the Cauchy problem of the system of discrete Boltzmann equations of the form ∂_tf_i+(f^{m_i}_i)_x=Q_i(f_1,f_2,...,f_n), (m_i > 1, i=1,...,n) with non-negative finite Radon measures as initial conditions. In particular, the existence and uniqueness of BV solutions for the above problem are obtained.

  • Keywords

System of discrete Boltzmann equations BV solutions existence and uniqueness

  • AMS Subject Headings

35L80 35L60 34A12 74G20 35B40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-22-127, author = {Hongjun Yuan and Yan Han }, title = {Existence and Uniqueness of BV Solutions for a Class of Degenerate Boltzmann Equations with Measures as Initial Conditions}, journal = {Journal of Partial Differential Equations}, year = {2009}, volume = {22}, number = {2}, pages = {127--152}, abstract = {

The existence and uniqueness of the solutions for the Boltzmann equations with measures as initial value are still an open problem which is posed by P. L. Lions (2000). The aim of this paper is to discuss the Cauchy problem of the system of discrete Boltzmann equations of the form ∂_tf_i+(f^{m_i}_i)_x=Q_i(f_1,f_2,...,f_n), (m_i > 1, i=1,...,n) with non-negative finite Radon measures as initial conditions. In particular, the existence and uniqueness of BV solutions for the above problem are obtained.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5251.html} }
TY - JOUR T1 - Existence and Uniqueness of BV Solutions for a Class of Degenerate Boltzmann Equations with Measures as Initial Conditions AU - Hongjun Yuan & Yan Han JO - Journal of Partial Differential Equations VL - 2 SP - 127 EP - 152 PY - 2009 DA - 2009/05 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5251.html KW - System of discrete Boltzmann equations KW - BV solutions KW - existence and uniqueness AB -

The existence and uniqueness of the solutions for the Boltzmann equations with measures as initial value are still an open problem which is posed by P. L. Lions (2000). The aim of this paper is to discuss the Cauchy problem of the system of discrete Boltzmann equations of the form ∂_tf_i+(f^{m_i}_i)_x=Q_i(f_1,f_2,...,f_n), (m_i > 1, i=1,...,n) with non-negative finite Radon measures as initial conditions. In particular, the existence and uniqueness of BV solutions for the above problem are obtained.

Hongjun Yuan and Yan Han . (2009). Existence and Uniqueness of BV Solutions for a Class of Degenerate Boltzmann Equations with Measures as Initial Conditions. Journal of Partial Differential Equations. 22 (2). 127-152. doi:
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