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Following the work on non-stationary fractal interpolation (Mathematics 7, 666 (2019)), we study non-stationary or statistically self-similar fractal interpolation on the Sierpiński gasket (SG). This article provides an upper bound of box dimension of the proposed interpolants in certain spaces under suitable assumption on the corresponding Iterated Function System. Along the way, we also prove that the proposed non-stationary fractal interpolation functions have finite energy.

We study a class of initial value problems for impulsive nonlinear wave equations. A new topological approach is applied to prove the existence of at least one and at least two nonnegative classical solutions. To prove our main results we give a suitable integral representation of the solutions of the considered problem. Then, we construct two operators so that any fixed point of their sum is a solution.

For one spatial variable, a new kind of coupled system for nonlinear wave equations of Emden-Fowler type is considered with boundary value and initial values. Under certain conditions on the initial data and the exponent $\rho$, we show that the viscoelastic terms lead our problem to be dissipative and that the global solutions cannot exist in $L^2$ beyond the given finite time i.e., \[ \int_{r_1}^{r_2} \Big( \vert u_1 \vert^2 + \vert u_2 \vert^2 \Big) \, dx \to +\infty \quad \hbox{ as } t\to T^{\ast}, \] where \[ \ln T^{\ast} = \frac{2}{\rho+1} \Big( \sum_{i=1}^2 \int_{r_1}^{r_2} \vert u_{i0} \vert^2 \, dx \Big) \Big( \sum_{i=1}^2 \int_{r_1}^{r_2} \left( 2u_{i0}u_{i1} - \vert u_{i0} \vert^2 \right) \, dx\Big)^{-1}. \]

The article discusses the effect of weak and strong damping terms on decay rate for systems of nonlinear m- wave equations with new viscoelastic structures. The factors that allowed system (1.1) to coexist for a long time are the strong nonlinearities in the sources. We showed, under a novel condition on the kernel function in (2.4), a new scenario for energy decay in (3.7) by using an appropriate energy estimates. This result extend the results in [18,27] for system of m-equations inspired from the paper [1].

Under some given conditions, we prove the explosion result of the solution of the system of nonlocal singular viscoelastic with damping and source terms on general case. This current study is a general case of the previous work of Boulaaras.

In this paper, we consider an initial boundary value problem for nonlinear Love equation with infinite memory. By combining the linearization method, the Faedo–Galerkin method, and the weak compactness method, the local existence and uniqueness of weak solution is proved. Using the potential well method, it is shown that the solution for a class of Love-equation exists globally under some conditions on the initial datum and kernel function.

The importance of the present study stems from the problematic nature of the marital relationships and the societal dimensions that stimulate some wives to murder their husbands with intention in Egypt. Hence, the question of this study runs so: What are the motives and societal dimensions that stimulate the wives to kill their husbands in Egypt? In order to find answers to this main question, the study makes use of the diagnostic and analytical approach with its two aspects: the qualitative and quantitative. That is to realize the aims of the study and to identify the dimensions of wives' violence in Egyptian society in addition to determining the factors that produce violence in the Egyptian family. The study also adopts the comprehensive investigation and scanning of the statistical crime reports of the public security administration associated with the ministry of internal affairs in Egypt in the period from 1985 to 2008. This helps in counting the rates of this crime, defining its types, classifying it in terms of general or familial, and comparing it with the crime of "murder with intention." The field study was carried out in Al-Qnater Al-Khairia prison for women, taking into consideration this prison as the main prison for female criminals. The study also employs so-called "depth interviews" in order to apply the questionnaire as the main tool capable of identifying the daily life aspects of the subject under study and their familial histories. The study was carried out between July 2009 and December 2009 in Al-Qnater Al-Khairia prison for women. The writing of the report occurred between January 2010 and July 2010. The study emphasizes that the reason behind the increase in the crime ratios lies in an inequality in the distribution of economic resources. This cause is the main factor in committing both the crimes motivated by money gain and violence. The results of the social surveys reveal that the murdering wife afiliates to the lower social class by a ratio of 83.33% of the total crimes (or 30 cases). 10% of those murderers belong to the upper lower class and 6.67% belong to the middle class. The latter are only two cases. The study reports that 53.33% of the female murderers do not have jobs and 46.67% of them are service workers. [ABSTRACT FROM AUTHOR]