Under suitable conditions we are able to solve the semilinear wave equation in any dimension. We are also able to compute the essential spectrum of the linear wave operator for the rotationally invariant periodic case.

where: x is position in one or more spatial dimensions; u(x, t) is some scalar or vector field, such as fluid velocity and pressure; L is a dissipative linear operator, such as ∇; f(u) includes other autonomous terms representing nonlinear advection, reaction, etc.; and q(u, t) is some time dependent control or possibly stochastic forcing [22]. Among many physically relevant examples are Burger...

The linear quadratic (LQ) optimal control problem is studied for a partial differential equation model of a time-varying plug flow tubular reactor. First some properties of the linearized model around a specific equilibrium profile are studied. Next, an LQ-control feedback is computed by using the corresponding operator Riccati differential equation, whose solution can be obtained via a related...

In this project, we consider minimizing multiple linear objective functions under a max-t-norm fuzzy relational equation constraint. Since the feasible domain of a max-Archimedean t-norm relational equation constraint is generally nonconvex, traditionally mathematical programming techiniques may have difficulty in yielding efficient solutions for such problems. In this paper, we apply the two-p...

Assume that $mathbb{D}$ is the open unit disk. Applying Ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{G}(alpha)$ and $mathcal{F}(mu)$ as follows begin{equation*}  mathcal{G}(alpha):=left{fin mathcal{A}:mathfrak{Re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right) <1+frac{alpha }{2},quad 0<alphaleq1right}, end{equation*} and begin{equation*}  ma...

A sequence of approximate linear collision models for hard-sphere and inverse-power-law gases is introduced. These models are obtained by expanding the linearized Boltzmann collision operator into a Hermite series, and a practical algorithm is proposed for evaluating the coefficients in the series. The sequence approximates the linearized Boltzmann operator to high accuracy, and it establishes ...

For a given nonzero bounded linear operator A on a Banach space X, we show that if A or A∗ has an eigenvalue then, except when the dimension of X is equal to two and the trace of A is zero, there exists a bounded linear operator B on X such that (i) AB + BA is of rank one, and (ii) I + f (A)B is invertible for every function f analytic in a neighborhood of the spectrum of A. This result was mot...

In this article, we study the asymptotical stability in p-th moment of mild solutions to a class of fractional impulsive partial neutral stochastic integro-differential equations with state-dependent delay in Hilbert spaces. We assume that the linear part of this equation generates an α-resolvent operator and transform it into an integral equation. Sufficient conditions for the existence and as...

We consider the problem of convergence and error estimation of the method for computing indefinite integrals proposed in [P. Keller, A method for indefinite integration of oscillatory and singular functions, Numerical Algorithms 46(3) (2007), 219–251]. To this end, we have analysed the properties of the difference operator related to the difference equation for the Chebyshev coefficients of a f...

Abstract. An operator-splitting algorithm is presented for the solution of a partial differential equation arising in the modeling of deposition processes in sand mechanics. Sand piles evolution is modeled by an advection-diffusion equation, with a non-smooth diffusion operator that contains a point-wise constraint on the gradient of the solution. Piecewise linear finite elements are used for t...