Generic transversality property for a class of wave equations with variable damping

A numerical solution of variable order diusion and wave equations

In this work, we consider variable order difusion and wave equations. The derivative is describedin the Caputo sence of variable order. We use the Genocchi polynomials as basic functions andobtain operational matrices via these polynomials. These matrices and collocation method help usto convert variable order diusion and wave equations to an algebraic system. Some examples aregiven to show the...

Wave equations with non-dissipative damping

Smooth attractors for the quintic wave equations with fractional damping

Dissipative wave equations with critical quintic nonlinearity and damping term involving the fractional Laplacian are considered. The additional regularity of energy solutions is established by constructing the new Lyapunov-type functional and based on this, the global well-posedness and dissipativity of the energy solutions as well as the existence of a smooth global and exponential attractors...

A numerical algorithm for solving a class of matrix equations

In this paper, we present a numerical algorithm for solving matrix equations $(A otimes B)X = F$  by extending the well-known Gaussian elimination for $Ax = b$. The proposed algorithm has a high computational efficiency. Two numerical examples are provided to show the effectiveness of the proposed algorithm.

Exponential Stability of Wave Equations with Potential and Indefinite Damping

First, we consider the linear wave equation utt−uxx +a(x)ut + b(x)u = 0 on a bounded interval (0, L) ⊂ R. The damping function a is allowed to change its sign. If a := 1 L R L 0 a(x)dx is positive and the spectrum of the operator (∂xx− b) is negative, exponential stability is proved for small ‖a− a‖L2 . Explicit estimates of the decay rate ω are given in terms of a and the biggest eigenvalue of...