Well-Posedness and Blow-Up of Solutions for a Variable Exponent Nonlinear Petrovsky Equation

Ercan ÇELİK

In this article, we investigate a nonlinear Petrovsky equation with variable exponent and damping terms. First, we establish the local existence using the Faedo-Galerkin approximation method under the conditions of positive initial energy and appropriate constraints on the variable exponents p & sdot; and q & sdot;. Finally, we prove a finite-time blow-up result for negative initial energy. Keyword: global existence; wave-equation

Existence, Decay, and Blow-up of Solutions for a Weighted m -Biharmonic Equation with Nonlinear Damping and Source Terms

Ercan ÇELİK

In this paper, we consider the weighted m-biharmonic equation with nonlinear damping and source terms. We proved the global existence of solutions. Later, the decay of the energy is established by using Nakao's inequality. Finally, we proved the blow-up of solutions in finite time.

Harr-NMF Feature Extraction for Multilevel Educational Technology Teaching Big Data System

An essential role in improving educational informatization and encouraging new approaches to education is played by educational technology, a specialist field that supports both theorising and doing in this area. When it comes to learning educational technology, students must have excellent professional knowledge and abilities, as well as a thorough understanding of data. Harr-NMF feature extraction for educational technology teaching large data systems is the focus of this project. With the help of big data technology, the construction of a teaching resource sharing system provides useful sol ...More

Application of Virtual Reality Technology in Visual Optimization of Product Appearance Design

Virtual reality technology is used in this research to perform an in-depth investigation and the analysis of visual optimization of product appearance design, as well as to adapt evolving technology to practical design. The breadth of virtual display technology may be further investigated, and software abilities can be enhanced by studying the virtual display of intelligent goods. The performance indicators of the product may be exhibited in an all-around manner via the virtual display, giving customers an intuitive experience and thereby stimulating consumers' desire to purchase. To achieve t ...More