Abstract: In the present paper, we construct the traveling wave solutions involving parameters for the (2+1)-dimensional cubic Klein-Gordon equation (cKG) via Enhanced (G’/G)-expansion method. The efficiency of this method for finding these exact solutions has been demonstrated. As a result, a set of solitary wave solutions are derived, which are expressed by the combinations of rational, hyperbolic and trigonometric functions involving several parameters. It is shown that the method is effective and can be used for many other nonlinear evolution equations (NLEEs) in mathematical physics.

Abstract: In this work, we are interested to obtain some result of existence and nonexistence of large positive weak solution for the following p-laplacian system where λ, µ and ν are a positive parameter, and Ω is a bounded domain in with smooth boundary ∂Ω. The proof of the main results is based to the sub-supersolutions method.

Abstract: In this paper a solution of the direct Cauchy problems for heat equation is founded in the form of Hermite polynomial series. A well-known classical solution of direct Cauchy problem is represented as Poisson's integral. The author reveals, the formulas obtained by him for solution of the inverse Cauchy problems have a symmetry with respect to the formulas for corresponding direct Cauchy problems. Obtained formulas for solution of the inverse problems can serve as a basis for reg-ularizing computational algorithms while well-known classical formula for the solution of the inverse Cauchy problem can't be a basis for regu-larizing computational algorithms.

Abstract: This paper takes the mathematical software Maple as the auxiliary tool to study the partial differential problems of two types of two-variables functions. We can obtain the infinite series forms of any order partial derivatives of these two types of functions by using differentiation term by term theorem, and hence greatly reduce the difficulty of calculating their higher order partial derivative values. On the other hand, we propose two examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying our answers by using Maple.

Abstract: We study in this article the boundary observability and the exact controllability for a problem of transmission. The system is governed by the wave equation with Wentzell dynamic artificial condition on the boundary. The geometrical domains considered are polyhedrons or polygons.

Abstract: Anisotropy is a property of some materials in which the physical properties vary with different crystallographic orientations. In this study, the analytical steady state solution to the anisotropic heat conduction in an orthotropic sphere is presented. There is a point heat source in the center of the sphere which supply the constant thermal energy. Using a transformation can change the anisotropic problem to an isotropic one which can be solved by the change of variables. The results showed that the isothermal surfaces are concentric ellipsoids which approach spheres while the conductivities in different directions are close to each other. The analytical results were validated with the 2D experimental tests performed for quartz as an orthotropic material. Despite the isotropic materials, it can be seen that the vectors of temperature gradients and the heat flux q are not parallel.

Abstract: Using variational methods, we study the existence of weak solutions for the degenerate quasilinear elliptic system where is a smooth bounded domain, stands for the gradient of -function , the weights are allowed to vanish somewhere, the primitive is intimately related to the first eigenvalue of a corresponding quasilinear system.

Abstract: We study the nonuniformly elliptic, nonlinear system Under growth and regularity conditions on the nonlinearities f and g, we obtain weak solutions in a subspace of the Sobolev space by applying a variant of the Mountain Pass Theorem.

Abstract: This paper investigates the inverse problem of simultaneously determining the time-dependent thermal diffusivity and the temperature distribution in a parabolic equation in the case of nonlocal boundary conditions containing a real parameter and integral overdetermination conditions. Under some consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the classical solution are shown by using the generalized Fourier method.

Abstract: The purpose of this seminar paper is to introduce the Fourier transform methods for partial differential equations. The introduction contains all the possible efforts to facilitate the understanding of Fourier transform methods for which a qualitative theory is available and also some illustrative examples was given. The resulting Fourier transform maps a function defined on physical space to a function defined on the space of frequencies, whose values quantify the “amount” of each periodic frequency contained in the original function then inverse Fourier transform reconstructs the original function from its transform.