The large-time behavior of the scalar, genuinely nonlinear Lax-Friedrichs scheme
The large-time behavior of the scalar, genuinely nonlinear Lax-Friedrichs scheme
We study the Lax-Friedrichs scheme, approximating the scalar, genuinely nonlinear conservation law <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u Subscript t Baseline plus f Subscript x Baseline left-parenthesis u right-parenthesis equals 0"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>u</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:mrow> <mml:mo>+</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>x</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>u</mml:mi> …