Blow up of solutions for a nonlinear viscoelastic system with general source term

Blowing Up for the p -Laplacian Parabolic Equation with Logarithmic Nonlinearity

“…For example, it is found in edge detection and optical elasticity, materials science, engineering, physics, and photonics. In addition, many works and problems in applied sciences have been designed and proposed by means of partial differential equations, including the modeling of some dynamic systems in physics and engineering ( [1][2][3][4][5][6][7][8][9][10][11][12][13]).…”

“…Motivated by the last recent mentioned works, here, we investigated problem (1) with the nonlinear diffusion Δ p = div ðj∇uj p−2 ∇uÞ and logarithmic nonlinearity juj p−2 u ln juj which extends problem in [14]. Our goal is to blow up solutions for problem (1) in order to put some preliminaries. More precisely, we give the blow-up result.…”