Titlebook: Introduction to Partial Differential Equations; David Borthwick Textbook 2016 Springer Nature Switzerland AG 2016 linear equations.partial

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Maximum Principles,In this chapter we will consider another approach to issues of uniqueness and stability, based on maximum values. This method applies generally to elliptic equations, which describe equilibrium states, and to parabolic equations, which are generally used to model diffusion.

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Weak Solutions,As noted in Sect. ., it is possible to define weak solutions of a PDE that are not sufficiently differentiable to solve the equation literally. In this chapter we will discuss the mathematical formulation of this generalized notion of solution.

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Variational Methods,In this chapter we will develop a strategy that involves reformulating a PDE in terms of a minimization problem on a function space.

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Distributions,To define weak derivatives in Chap. ., we measured the values of a solution using test functions. Taking this idea one step further leads to a generalization of the concept of a function, called a distribution.

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David BorthwickPerfect book for a ?One-semester PDE course.Includes a thorough discussion of modeling process for each equation.Covers indepth three types of linear PDES: elliptic, parabolic, and hyperbolic?.Include

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