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Global asymptotics toward the rarefaction wave for solutions of viscous ๐‘-system with boundary effect

Global asymptotics toward the rarefaction wave for solutions of viscous ๐‘-system with boundary effect

The initial-boundary value problem on the half-line <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R Subscript plus Baseline dot equals left-parenthesis 0 comma normal infinity right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>R</mml:mi> <mml:mo>+</mml:mo> </mml:msub> </mml:mrow> <mml:mo>โ‹…</mml:mo> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">โˆž</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">{R_ + } \cdot = โ€ฆ