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The authors of this paper study singular phenomena(vanishing and blowing-upin finite time) of solutions to the homogeneous $\hbox{Dirichlet}$ boundaryvalue problem of nonlinear diffusion equations involving$p(x)$-\hbox{Laplacian} operator and a nonlinear source. The authors discusshow the value of the variable exponent $p(x)$ and initial energy(data) affectthe properties of solutions. At the same time, we obtain the criticalextinction and blow-up exponents of solutions.

Singular Phenomena of Solutions for Nonlinear Diffusion Equations involving $p(x)$-\hbox{Laplacian} Operator