Analysis of the Stability of the Riemann Problem for a Simplified Model in Magnetogasdynamics

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/amp/volume-2016/7526413/figures/7526413.fig.009a.svgz" name="7526413.fig.009a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>A perturbed solution in the neighborhood of the origin (<svg height="8.98582pt" id="M247" style="vertical-align:-0.6370001pt" version="1.1" viewbox="-0.0498162 -8.34882 25.736 8.98582" width="25.736pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,8.065,0)"><path d="M512 230V281L75 514V456L453 256V254L75 55V-3L512 230Z" id="g117-92"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,19.328,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg>)</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/amp/volume-2016/7526413/figures/7526413.fig.009b.svgz" name="7526413.fig.009b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>A perturbed solution in the neighborhood of the origin (<svg height="8.98582pt" id="M248" style="vertical-align:-0.6370001pt" version="1.1" viewbox="-0.0498162 -8.34882 25.736 8.98582" width="25.736pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,8.065,0)"><path d="M512 230V281L75 514V456L453 256V254L75 55V-3L512 230Z" id="g117-92"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,19.328,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg>)</td></tr></table>

Advances in Mathematical Physics

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Figure 9

Figure 9: Analysis of the Stability of the Riemann Problem for a Simplified Model in Magnetogasdynamics 