The particle growth term renders hyperbolic the dynamic population balance equation. Problems associated with the numerical solution of hyperbolic partial differential equations with stationary grid methods are well known. Moreover in the common case of combined molecular particle growth and coagulation. the convolution integral of the coagulation terms makes the moving grid methods computation...

In this paper, which is essentially a survey, we solve the global Cauchy problem on causal manifolds for hyperbolic systems of linear partial differential equations in the framework of hyperfunctions. Besides the classical Cauchy–Kowalevsky theorem, our proofs only use tools and ideas of purely algebraic and geometric nature from the microlocal theory of sheaves. Mathematics Subject Classificat...

Nonlocal problems for hyperbolic equations of the first order describe the dynamic of population [1]–[3]. During the last thirty years the existence and uniqueness of the solution of nonlocal problems for the system of hyperbolic equations have been considered in a number of papers [4]–[8]. The authors assumed that the nonlinear functions satisfy the Lipschitz condition with respect to the unkn...

The hyperbolic partial differential equation with an integral condition arises in many physical phenomena. In this research a numerical technique is developed for the one-dimensional hyperbolic equation that combine classical and integral boundary conditions. The proposedmethod is based on shifted Legendre tau technique. Illustrative examples are included to demonstrate the validity and applica...

Pseudo-differential and Fourier series operators on the torus T = (R/2πZ) are analyzed by using global representations by Fourier series instead of local representations in coordinate charts. Toroidal symbols are investigated and the correspondence between toroidal and Euclidean symbols of pseudo-differential operators is established. Periodization of operators and hyperbolic partial differenti...

The phase space for nonlinear hyperbolic functional differential equations with unbounded delay is constructed. The set of axioms for generalized solutions of initial problems is presented. A theorem on the existence and continuous dependence upon initial data is given. The Cauchy problem is transformed into a system of integral functional equations. The existence of solutions of this system is...

We prove the unique solvability of boundary-value problem for a loaded third-order integrodifferential equation with parabolic-hyperbolic operator. By method integral equations, we existence and uniqueness solutions problems.

The present paper focuses on numerical study for an inclined magneto-hydrodynamic effect on free convection flow of a tangent hyperbolic nanofluid embedded with Carbon nanotubes (CNTs) over a stretching surface taking velocity and thermal slip into account. Two types of nanoparticles are considered for the study; they are single and multi-walled nanotubes. The presentation of single-parameter g...