Blow-Up of Solutions for a Coupled Nonlinear Viscoelastic Equation with Degenerate Damping Terms: Without Kirchhoff Term

In this work, we consider a quasilinear system of viscoelastic equations with degenerate damping and source terms without the Kirchhoff term. Under suitable hypothesis, we study the blow-up of solutions.

Existence of Solutions for a Quasilinear System with Gradient Terms

In this paper, it is considered the existence of solutions for a quasilinear system involving the p-Laplacian operator and gradient terms. The approach is based on sub-supersolution arguments and the Schauder's Fixed Point Theorem. The results in this paper allow to consider several growth conditions in the gradient and complete some recent contributions.

Blow-up of solutions for a quasilinear system with degenerate damping terms

In this work, we consider a quasilinear system of viscoelastic equations with degenerate damping and general source terms. According to some suitable hypothesis, we study the blow-up of solutions. This is the general case of the recent results of Boulaaras’ works (Bull. Malays. Math. Sci. Soc. 43:725–755, 2020) and (Appl. Anal. 99:1724–1748, 2020).

A reaction-diffusion-advection competition model with a free boundary

In this paper, we study a competitive diffusion quasilinear system with a free boundary. First, we investigate the mathematical questions of the problem. A priori estimates of Schauder type are established, which are necessary for the solvability of the problem. One of two competing species is an invader, which initially exists on a certain sub-interval. The other is initially distributed throughout the area under consideration. Examining the influence of baseline data on the success or failure of the first invasion. We conclude that there is a dichotomy of spread and extinction and give precise criteria for spread and extinction in this model.

Global Existence and General Decay of Solutions for a Quasilinear System with Degenerate Damping Terms

In this work, we consider a quasilinear system of viscoelastic equations with degenerate damping, dispersion, and source terms under Dirichlet boundary condition. Under some restrictions on the initial datum and standard conditions on relaxation functions, we study global existence and general decay of solutions. The results obtained here are generalization of the previous recent work.

Bifurcation Results for a Fractional Quasilinear System with Critical Nonlinearities

In this paper, we prove bifurcation results for a fractional quasilinear system with critical nonlinearities. Under different assumptions on the exponents of nonlinearities, we give existenceresults respectively.

On the evolution of acceleration discontinuities in van der Waals dusty magnetogasdynamics

The article presents the study of the evolutionary behavior of plane and cylindrically symmetric acceleration discontinuities along the characteristic path under the effect of dust particles in a non-ideal magnetogasdynamic flow. Implications regarding the propagation of disturbances in planar and cylindrically symmetric flows have been shown. Using the characteristics of the governing quasilinear system as a reference coordinate system, we transform the fundamental equations and find the solution. It is explored how the dust particles, along with the nonideal parameter, will influence the steepening or flattening of the propagating waves in magnetic and nonmagnetic cases. The transport equation leading to the evolution of acceleration discontinuities is determined, which provides the relation for the occurrence of shock. The impact of non-idealness of the gas and dust on the evolutionary process of propagating waves for the magnetic and nonmagnetic cases are discussed. The comparison between the flow patterns and distortion of the propagating waves for planar and cylindrically symmetric flows is demonstrated under the various parameter effects.