Galoitica: Journal of Mathematical Structures and Applications

In this work, we study the regularization method for solving the Boundary Value Problem (BVP) for heat equation. The discretization method applied with two variables on Volterra integral equation in order to covert the problem into a linear operator equation after applied the separation of variables method to solve the partial differential equation. The regularization way used to obtain the estimate solution by using the Lavrentiev regularization method.

In this research, the Karmarker's method of linear programming was improved using the eigenvector of the starting point with all iterations.Where the improvement showed that Karmarker's method can be reduced in a theoretical way by direct method without iterations and access to the optimal solution. The procedure was also Comparison of the two methods and the results of the proposed method were faster and better to reach.

An implicative BCI algebra is a non empty set X with a special element O and a binary operation * with many clear conditions.In this work, we study the topological space  and present some properties especially the compactness and connection. Also, we prove that it is a Hausdorff space and regular.

In this paper, we study the global existence and the asymptotic behaviour for the solutions of the following non-linear and non-homogeneous differential equation with order 3 and with a Laplacian p≥1 〖〖〖〖[|u〗^(ˊˊ) (t)|〗^(p-1) u〗^(ˊˊ) (t)]〗^ˊ+f(t,u(u))=e(t)  ;p≥1   Where t→+∞. Also, we get the solutions of (1), which the type of the asymptotic behaviour of the global solutions is at^2+bt+c; t→+∞, a,b,c ∈R ;a ≠0

Most physical mathematical problems, when solved, turn into one or more partial differential equations with imposed initial conditions or boundary conditions . This is known as the boundary value problems of differential equations .This research studies the solution of the set of Partial Differential Equations of parabolic and hyperbolic-hyperbolic type with boundary conditions imposed in different regions of the plane x o y . This research has been proving the theorem of uniqueness and the existence of the solution.