Global Existence and Decay Estimates of Energy of Solutions for a New Class of $p$-Laplacian Heat Equations with Logarithmic Nonlinearity

Abstract

The present research paper is related to the analytical studies of p -Laplacian heat equations with respect to logarithmic nonlinearity in the source terms, where by using an efficient technique and according to some sufficient conditions, we get the global existence and decay estimates of solutions.

Analytical Properties of the Generalized Heat Matrix Polynomials Associated with Fractional Calculus

“…whose last summation, in view of ( 11), is easily seen to arrive at the expression in (32). This completes the proof of Theorem 17.…”

“…Further, the generalized heat polynomials are mainly used to construct an approximate solution of a given problem as a linear combination of the polynomials. Such solution satisfies the governing equation and other equations (cf., e.g., [30][31][32][33][34][35]).…”

Blow-Up Results for a Class of Quasilinear Parabolic Equation with Power Nonlinearity and Nonlocal Source

“…Problem (1) appears in the study of fluid flow through porous media with integral source (see [3,4]) and population dynamics (see [5,6]). Actually, equations of the above form are mathematical models occurring in studies of the p-Laplace equation ( [7][8][9][10][11][12][13][14][15] and references therein), generalized reaction-diffusion theory [16], non-Newtonian fluid theory [17,18], non-Newtonian filtration theory [19,20], and the turbulent flow of a gas in porous medium [7]. Media with p > 2 are called dilatant fluids and those with p < 2 are called pseudoplastics.…”

Unsteady Electrohydrodynamic Stagnation Point Flow of Hybrid Nanofluid Past a Convective Heated Stretch/Shrink Sheet

“…The reader can further study about heat transfer through nanofluid flow in Refs. [33][34][35][36][37][38][39][40].…”