parabolic differential equation

parabolic differential equation

[¦par·ə¦bäl·ik ‚dif·ə′ren·chəl i′kwā·zhən]
(mathematics)
A general type of second-order partial differential equation which includes the heat equation and has the form where the Ai j , Bi , C, and F are suitably differentiable real functions of x1, x2, …, xn , and there exists at each point (x1, …, xn ) a real linear transformation on the xi which reduces the quadratic form to a sum of fewer than n squares, not necessarily all of the same sign, while the same transformation does not reduce the Bi to 0. Also known as parabolic partial differential equation.
References in periodicals archive ?
(17) In the paper titled "A Compact Difference Scheme for Solving Fractional Neutral Parabolic Differential Equation with Proportional Delay," a linearized compact finite difference scheme was constructed for solving the fractional neutral parabolic differential equation with proportional delay.
Some oscillation results are also given for the delay parabolic differential equation as follows:
Jones, "Determination of a coefficient in a parabolic differential equation, I.
In this paper, we consider the following fractional neutral parabolic differential equation with proportional delay:
Liu, "Inverse coefficient problems for nonlinear parabolic differential equations," Acta Mathematica Sinica, vol.
Tian, "Asymptotic stability analysis of the linear [theta]-Method for linear parabolic differential equations with delay," Journal of Difference Equations and Applications, vol.
Lin, "Determination of a parameter p(t) in some quasi-linear parabolic differential equations," Inverse Problems, vol.
We notice that in all later published papers the theory of the finite difference method for the parabolic differential equations with various types of nonlocal conditions was created as fully-implicit or explicit schemes theory.
Zhang, "A compact difference scheme combined with extrapolation techniques for solving a class of neutral delay parabolic differential equations," Applied Mathematics Letters, vol.
Sun, "A Crank-Nicolson scheme for a class of delay nonlinear parabolic differential equations," Journal on Numerical Methods and Computer Applications, vol.
Simultaneous space-time adaptive wavelet solution of nonlinear parabolic differential equations. J.
On nonexistence of global solutions of some semilinear parabolic differential equations. Proceedings of the Japan Academy, 49(7):503-505, 1973.