Global C1 Solution to the Initial-boundary Value Problem for Diagonal Hyperbolic Systems with Linearly Degenerate Characteristics

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Volume 16, Issue 1

Tatsien Li & Yuejun Peng

J. Part. Diff. Eq., 16 (2003), pp. 8-17.

Published online: 2003-02

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Abstract

We prove that the Cº boundedness of solution implies the global existence and uniqueness of C¹ solution to the initial-boundary value problem for linearly degenerate quasilinear hyperbolic systems of diagonal form with nonlinear boundary conditions. Thus, if the C¹ solution to the initial-boundary value problem blows up in a finite time, then the solution itself must tend to the infinity at the starting point of singularity.

Keywords

Initial-boundary value problem global C¹ solution quasilinear hyperbolic system of diagonal form linearly degenerate characteristics

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@Article{JPDE-16-8, author = {}, title = {Global C1 Solution to the Initial-boundary Value Problem for Diagonal Hyperbolic Systems with Linearly Degenerate Characteristics}, journal = {Journal of Partial Differential Equations}, year = {2003}, volume = {16}, number = {1}, pages = {8--17}, abstract = { We prove that the Cº boundedness of solution implies the global existence and uniqueness of C¹ solution to the initial-boundary value problem for linearly degenerate quasilinear hyperbolic systems of diagonal form with nonlinear boundary conditions. Thus, if the C¹ solution to the initial-boundary value problem blows up in a finite time, then the solution itself must tend to the infinity at the starting point of singularity.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5401.html} }

TY - JOUR T1 - Global C1 Solution to the Initial-boundary Value Problem for Diagonal Hyperbolic Systems with Linearly Degenerate Characteristics JO - Journal of Partial Differential Equations VL - 1 SP - 8 EP - 17 PY - 2003 DA - 2003/02 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5401.html KW - Initial-boundary value problem KW - global C¹ solution KW - quasilinear hyperbolic system of diagonal form KW - linearly degenerate characteristics AB - We prove that the Cº boundedness of solution implies the global existence and uniqueness of C¹ solution to the initial-boundary value problem for linearly degenerate quasilinear hyperbolic systems of diagonal form with nonlinear boundary conditions. Thus, if the C¹ solution to the initial-boundary value problem blows up in a finite time, then the solution itself must tend to the infinity at the starting point of singularity.

Tatsien Li & Yuejun Peng . (2019). Global C1 Solution to the Initial-boundary Value Problem for Diagonal Hyperbolic Systems with Linearly Degenerate Characteristics. Journal of Partial Differential Equations. 16 (1). 8-17. doi:

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