Answer to Question #11273 in Mechanics | Relativity for ruchi

Question

describe poisson and laplas equation.

Answer 1

In mathematics, Poisson's (<img class="tex" alt="\Delta\varphi=f" src="https://upload.wikimedia.org/wikipedia/en/math/5/c/1/5c1eca5688ddbfe8e4df96b205f652ed.png">)equation
is a partial differential equation of elliptic type with broad utility in
electrostatics, mechanical engineering and theoretical physics.In mathematics,
Laplace's(<img style="BORDER-BOTTOM-STYLE: none; LINE-HEIGHT: 19px; BORDER-LEFT-STYLE: none; FONT-FAMILY: sans-serif; BORDER-TOP-STYLE: none; BORDER-RIGHT-STYLE: none; FONT-SIZE: 13px; VERTICAL-ALIGN: middle" class="tex" alt="\nabla^2 \varphi = 0 \," src="https://upload.wikimedia.org/wikipedia/en/math/4/2/6/42635da1dea70ee9c2f855a7c52573c9.png" data-mce-style="border-style: none; vertical-align: middle; font-family: sans-serif; font-size: 13px; line-height: 19px;" data-mce-src="https://upload.wikimedia.org/wikipedia/en/math/4/2/6/42635da1dea70ee9c2f855a7c52573c9.png">)
equation is a second-order partial differential equation.Laplace's equation and
Poisson's equation are the simplest examples of elliptic partial differential
equations. Solutions of Laplace's equation are called harmonic functions.The
general theory of solutions to Laplace's equation is known as potential theory.
The solutions of Laplace's equation are the harmonic functions, which are
important in many fields of science, notably the fields of electromagnetism,
astronomy, and fluid dynamics, because they can be used to accurately describe
the behavior of electric, gravitational, and fluid potentials. In the study of
heat conduction, the Laplace equation is the steady-state heat equation.