Bounded variation and Weak solution

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Difference between Bounded variation and Weak solution

Bounded variation vs. Weak solution

In mathematical analysis, a function of bounded variation, also known as function, is a real-valued function whose total variation is bounded (finite): the graph of a function having this property is well behaved in a precise sense. In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense.

Differentiable function

In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.

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Distribution (mathematics)

Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Hyperbolic partial differential equation

In mathematics, a hyperbolic partial differential equation of order n is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first derivatives.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Open set

In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.

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Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.

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Partial derivative

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).

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Partial differential equation

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Smoothness

In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.

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Support (mathematics)

In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero.

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