Nonlinear parabolic inequalities in Lebesgue-Sobolev spaces with variable exponent

On the well-posedness problem of the electrorheological fluid equations

“…If b(x) = 0, a(x) = 1 for all x ∈ , the existence and uniqueness results of Eq. (1.1) have been widely researched, one may refer to [2][3][4][5][6][7] and the references therein. If p(x) = p, the equations are known as non-Newtonian fluid equations, and have been studied by many mathematicians, one may refer to [8] and the references therein.…”

On an electrorheological fluid equation with orientated convection term

“…(Ω). Then there is a unique nonnegative solution u ε ∈ L p + (0, T; W 1,p + 0 (Ω)) [5], which satisfies…”

“…When p(x, t) > 1 is a measurable function on Q T , equation (1.1) arises in electrorheological fluids theory [1]. If f (x, t) = 0, a(x, t) = 1 for all (x, t) ∈ Q T , the existence and uniqueness results of equation (1.1) have been obtained in [2][3][4][5][6] etc. If p(x, t) = p > 1 is a constant, a(x, t) = 1 and f (x, t) = 0, equation (1.1) is well known as non-Newtonian fluid equation and has been studied by many mathematicians, one can refer to [7][8][9][10][11][12][13][14][15] and the references therein.…”

Entropy solutions for a nonlinear unilateral p(x) parabolic problems with f - div F data

“…Theorem 3.1. Under assumptions ( 8)- (11), there exists at least one entropy solution of problem (P):…”