Some properties of solutions for an evolution p(x)-Laplacian equation
We consider an initial-boundary value problem for an evolution p(x)-Laplacian equation. The problems describe the motion of generalized Newtonian fluids which were studied by some other authors. Under some assumptions on the initial value, we establish the existence of weak solutions by the time-discrete method. The uniqueness and the asymptotic behavior of solutions are also discussed.
Keywords and phrasesp(x)-Laplace existence uniqueness asymptotic behavior
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