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Volume 20, Issue 2
Life-span of Classical Solutions of Initial-boundary Value Problem for First Order Quasilinear Hyperbolic Systems

Hong Lu

J. Part. Diff. Eq., 20 (2007), pp. 131-154.

Published online: 2007-05

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  • Abstract

In this paper, we consider the mixed initial-boundary value problem for quasilinear hyperbolic systems with nonlinear boundary conditions in a half-unbounded domain {(t, x)|t ≥ 0, x ≥ 0}. Under the assumption that the positive eigenvalues are not all weakly linearly degenerate, we obtain the blow-up phenomenon of the first order derivatives of C¹ solution with small and decaying initial data. We also give precise estimate of the life-span of C¹ solution.

  • Keywords

Quasilinear hyperbolic system mixed initial-boundary value problem life-span weak linear degeneracy

  • AMS Subject Headings

35L50 35Q72 74K05.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-20-131, author = {}, title = {Life-span of Classical Solutions of Initial-boundary Value Problem for First Order Quasilinear Hyperbolic Systems}, journal = {Journal of Partial Differential Equations}, year = {2007}, volume = {20}, number = {2}, pages = {131--154}, abstract = {

In this paper, we consider the mixed initial-boundary value problem for quasilinear hyperbolic systems with nonlinear boundary conditions in a half-unbounded domain {(t, x)|t ≥ 0, x ≥ 0}. Under the assumption that the positive eigenvalues are not all weakly linearly degenerate, we obtain the blow-up phenomenon of the first order derivatives of C¹ solution with small and decaying initial data. We also give precise estimate of the life-span of C¹ solution.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5298.html} }
TY - JOUR T1 - Life-span of Classical Solutions of Initial-boundary Value Problem for First Order Quasilinear Hyperbolic Systems JO - Journal of Partial Differential Equations VL - 2 SP - 131 EP - 154 PY - 2007 DA - 2007/05 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5298.html KW - Quasilinear hyperbolic system KW - mixed initial-boundary value problem KW - life-span KW - weak linear degeneracy AB -

In this paper, we consider the mixed initial-boundary value problem for quasilinear hyperbolic systems with nonlinear boundary conditions in a half-unbounded domain {(t, x)|t ≥ 0, x ≥ 0}. Under the assumption that the positive eigenvalues are not all weakly linearly degenerate, we obtain the blow-up phenomenon of the first order derivatives of C¹ solution with small and decaying initial data. We also give precise estimate of the life-span of C¹ solution.

Hong Lu . (2019). Life-span of Classical Solutions of Initial-boundary Value Problem for First Order Quasilinear Hyperbolic Systems. Journal of Partial Differential Equations. 20 (2). 131-154. doi:
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