TY - JOUR
T1 - Traveling Waves and Capillarity Driven Spreading of Shear-thinning Fluids
JO - Journal of Partial Differential Equations
VL - 1
SP - 33
EP - 67
PY - 2010
DA - 2010/02
SN - 23
DO - http://doi.org/10.4208/jpde.v23.n1.3
UR - https://global-sci.org/intro/article_detail/jpde/5221.html
KW - Shear-thinning fluid
KW - traveling waves
AB - <p>We study capillary spreadings of thin films of liquids of power-law rheology. These satisfy u_t+(u^{λ+2}|u_{xxx}^{λ-1}u_{xxx})_x=0, where u(x,t) represents the thickness of the one-dimensional liquid and λ &gt; 1. We look for traveling wave solutions so that u(x,t)=g(x+ct) and thus g satisfies g&#39;&#39;&#39;=\frac{|g-ε|^\frac1λ}{g^{1+\frac2λ}}sgn(g-ε). We show that for each ε &gt; 0 there is an infinitely oscillating solution, g_ε, such that lim_{t→∞}g_ε=ε and that g_ε→g_0 as ε→ 0, where g_0 ≡ 0 for t ≥ 0 and g_0=c_λ|t|^{\frac{3λ}{2λ+1}} for t &lt; 0 &nbsp;for some constant c_λ.</p>