On a degenerate parabolic equation with Newtonian fluid?non-Newtonian fluid mixed type

نویسندگان

چکیده

Abstract We study the existence of weak solutions to a Newtonian fluid?non-Newtonian fluid mixed-type equation $$ {u_{t}}= \operatorname{div} \bigl(b(x,t){ \bigl\vert {\nabla A(u)} \bigr\vert ^{p(x) - 2}}\nabla A(u)+\alpha (x,t)\nabla A(u) \bigr)+f(u,x,t). u t = div ( b x , ) | ? A p ? 2 + ? f . assume that $A'(s)=a(s)\geq 0$ ? s a ? 0 , $A(s)$ is strictly increasing function, $A(0)=0$ $b(x,t)\geq and $\alpha (x,t)\geq . If b(x,t)=\alpha (x,t)=0,\quad (x,t)\in \partial \Omega \times [0,T], ? ? ? × [ T ] then we prove stability without boundary value condition.

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ژورنال

عنوان ژورنال: Journal of Inequalities and Applications

سال: 2021

ISSN: ['1025-5834', '1029-242X']

DOI: https://doi.org/10.1186/s13660-021-02550-w