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Disscus that the initial value problem (Cauchy problem) for the Laplace equation is not well-posed. It may be noted that a problem involving a PDE is well-posed if the following three properties are satisfied: (i) The solution to the problem exists. (ii) The solution is unique. (iii) The solution depends continuously on the data of the problem. Fortunately, many a physical phenomena give rise to initial or boundary or IBVPS which are well-posed.

Disscus that the initial value problem (Cauchy problem) for the Laplace equation is not well-posed. It may be noted that a problem involving a PDE is well-posed if the following three properties are satisfied: (i) The solution to the problem exists. (ii) The solution is unique. (iii) The solution depends continuously on the data of the problem. Fortunately, many a physical phenomena give rise to initial or boundary or IBVPS which are well-posed.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 47RE
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Disscus that the initial value problem (Cauchy problem) for the Laplace equation is not well-posed. It may be noted that a problem involving a PDE is well-posed if the following three properties are satisfied: (i) The solution to the problem exists. (ii) The solution is unique. (iii) The solution depends continuously on the data of the problem. Fortunately, many a physical phenomena give rise to initial or boundary or IBVPS which are well-posed.
Transcribed Image Text:Disscus that the initial value problem (Cauchy problem) for the Laplace equation is not well-posed. It may be noted that a problem involving a PDE is well-posed if the following three properties are satisfied: (i) The solution to the problem exists. (ii) The solution is unique. (iii) The solution depends continuously on the data of the problem. Fortunately, many a physical phenomena give rise to initial or boundary or IBVPS which are well-posed.
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