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PP. 6-12

Open Access

Enhanced (G’/G)-Expansion Method to Find the Exact Solutions of Nonlinear Evolution Equations in Mathematical Physics

Md. Ekramul Islam, Kamruzzaman Khan, M. Ali Akbar, Rafiqul Islam

International Journal of Partial Differential Equations and Applications. 2013, 1(1), 6-12

DOI: 10.12691/ijpdea-1-1-2

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.

Figure 2 of 4

PP. 13-17

Open Access

Existence and Nonexistence of Weak Positive Solution for Classes of 3 × 3 P-Laplacian Elliptic Systems

Guefaifia Rafik, Akrout Kamel, Saifia Warda

International Journal of Partial Differential Equations and Applications. 2013, 1(1), 13-17

DOI: 10.12691/ijpdea-1-1-3

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.

PP. 1-6

Open Access

On a New Formulas for a Direct and Inverse Cauchy Problems of Heat Equation

N. Yaremko, O. Yaremko

International Journal of Partial Differential Equations and Applications. 2014, 2(1), 1-6

DOI: 10.12691/ijpdea-2-1-1

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.

PP. 7-12

Open Access

Application of Differentiation Term by Term Theorem on the Partial Differential Problems

Chii-Huei Yu

International Journal of Partial Differential Equations and Applications. 2014, 2(1), 7-12

DOI: 10.12691/ijpdea-2-1-2

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.

PP. 13-22

Open Access

The Wave Equation with Dynamic Wentzell Boundary Condition in Polygonal and Polyhedral Domains: Observation and Exact Controllability

Tawfik Masrour

International Journal of Partial Differential Equations and Applications. 2014, 2(1), 13-22

DOI: 10.12691/ijpdea-2-1-3

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.