1. This paper will discuss the solution of an initial value problem of parabolic type.

2. The boundary - initial value problem is reduced to a boundary - value problem only.

3. The initial value problem for a nonlinear hyperbolic equation is studied. The existence and uniqueness of the global strong solution to the problem are proved.

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4. If the initial value function of an initial value problem is in the form of separated variables, then its exact solution is also in the form of separated variables.

5. The initial boundary value problem and initial value problem for the semilinear pseudo-hyperbolic integrodifferential equation are considered.

6. The other type of initial value problem of interest for us is the diffusion equation.

7. By initial value problem of differential equation, some functional equations are studied and some properties of the functional equations are obtained.

8. Next, formal approximations of initial value problem was constructed by perturbation method and the asymptotic validity of the formal approximation is got.

9. The traditional raytracing methods comprise the try-shooting method of the initial value problem and the bending method of the border value problem.

10. Upper lower solutions method and monotone iterative technique are applied to initial value problem.

11. The local existence and uniqueness of smooth solution of the periodic initial value problem for degenerate Landau-Lifshitz system of antiferromagnets in one dimension are proved.

12. For arbitrary large initial data, if it is away from vacuum, the smooth solutions to the initial value problem are uniformly (namely, independent of time) away from vacuum.

13. When the initial disturbance is in the asymptotically stable attractive region, the solution of the initial value problem of the quadratic delay discrete singular systems approaches zero.

14. Based on the research of orbit determination by using two GPS satellites, this paper discusses the initial value problem and provides an effective method of getting initial value.

15. And by using the property of derivatives of energy norms, the eigenproblem is transformed safely into a specific initial value problem of an ordinary differential equation.

16. Present the computer program for finding an analytic solution of well-posed barotropic primitive equations' general initial value problem.

17. We begin by recapitulating the complete list of equations for a mixed boundary - initial value problem.

18. Using the contraction mapping principle, we proved a theorem about the existence of solution for initial value problem of a class of implicit ordinary differential equations of the first order.

19. The motion of the blade is investigated by the numerical solution of a complex nonlinear initial value problem.

20. For certain initial conditions, we need only calculate their high order Laplace operator, then we can obtain the accurate solution of the initial value problem.

21. Based on theory of hyperbolic linear partial differential operator, the initial value problem of a kind of quasi-linear hyperbolic equations with non-zero initial values was introduced and studied.

22. Present the computer program for finding an analytic solution of well-posed atmospheric circulation equations' general initial value problem.