Global Existence, Exponential Decay and Blow-Up of Solutions for a Class of Fractional Pseudo-Parabolic Equations with Logarithmic Nonlinearity

Abstract

In this paper, we study the fractional pseudo-parabolic equations u t + (− )

Blow-up for a Porous Medium Equation with Local Linear Boundary Dissipation

“…The operational mechanism of this refrigeration system lies in the fact that the heat absorbed from the fluid is proportional to the power of the rate of change of the temperature, which can be expressed as: ¶u ¶n =-|u t | q -2 u t  x Î Γ 1  where ¶u ¶n stands for the heat flux from Ω to the fluid. Evolution equations [1][2][3][4][5][6][7][8] with boundary damping have attracted the attention of mathematicians in the past period. For instance, Fiscella and Vitillaro [9] studied the following problem with local nonlinear boundary dissipation…”