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 A_i_j, B_i, C, and F are suitably differentiable real functions of x₁, x₂, …, x_n, and there exists at each point (x₁, …, x_n) a real linear transformation on the x_iwhich 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 B_ito 0. Also known as parabolic partial differential equation.

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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.

Recent Development on Nonlinear Methods in Function Spaces and Applications in Nonlinear Fractional Differential Equations

Some oscillation results are also given for the delay parabolic differential equation as follows:

The oscillation of a class of the fractional-order delay differential equations

Jones, "Determination of a coefficient in a parabolic differential equation, I.

Identifying an unknown coefficient in the reaction-diffusion equation using He's VIM

In this paper, we consider the following fractional neutral parabolic differential equation with proportional delay:

A Compact Difference Scheme for Solving Fractional Neutral Parabolic Differential Equation with Proportional Delay

Liu, "Inverse coefficient problems for nonlinear parabolic differential equations," Acta Mathematica Sinica, vol.

An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy

Tian, "Asymptotic stability analysis of the linear [theta]-Method for linear parabolic differential equations with delay," Journal of Difference Equations and Applications, vol.

Linear [theta]-Method and Compact [theta]-Method for Generalised Reaction-Diffusion Equation with Delay

Lin, "Determination of a parameter p(t) in some quasi-linear parabolic differential equations," Inverse Problems, vol.

Identification of a Time-Dependent Coefficient in Heat Conduction Problem by New Iteration Method

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.

Semi-Implicit Difference Scheme for a Two-Dimensional Parabolic Equation with an Integral Boundary Condition

Zhang, "A compact difference scheme combined with extrapolation techniques for solving a class of neutral delay parabolic differential equations," Applied Mathematics Letters, vol.

High-order compact difference scheme for the numerical solution of time fractional heat equations

Sun, "A Crank-Nicolson scheme for a class of delay nonlinear parabolic differential equations," Journal on Numerical Methods and Computer Applications, vol.

A Crank-Nicolson difference scheme for solving a type of variable coefficient delay partial differential equations

Simultaneous space-time adaptive wavelet solution of nonlinear parabolic differential equations. J.

Adaptive Fup collocation method for time dependent partial differential equations

On nonexistence of global solutions of some semilinear parabolic differential equations. Proceedings of the Japan Academy, 49(7):503-505, 1973.

Fujita Critical Curve for a Coupled Diffusion System with Inhomogeneous Neumann Boundary Conditions