Consider the following 2nd order PDE, Uzz +2Uzy + 4U₂ = 0. (i) Write down its principal part and then determine the type (elliptic, parabolic or hyperbolic). (ii) Change the principal part of the above equation to a canonical form (i.e. without cross-derivatives).
Consider the following 2nd order PDE, Uzz +2Uzy + 4U₂ = 0. (i) Write down its principal part and then determine the type (elliptic, parabolic or hyperbolic). (ii) Change the principal part of the above equation to a canonical form (i.e. without cross-derivatives).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 34RE
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![Consider the following 2nd order PDE,
Uzz +2Uzy + 4U₂ = 0.
(i) Write down its principal part and then determine the type (elliptic, parabolic
or hyperbolic).
(ii) Change the principal part of the above equation to a canonical form (i.e.
without cross-derivatives).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7bc9583c-2eed-433e-b3be-99cb5345471a%2F948b2e52-f61d-4158-b6e5-939e8cf6d088%2F7e90xo_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following 2nd order PDE,
Uzz +2Uzy + 4U₂ = 0.
(i) Write down its principal part and then determine the type (elliptic, parabolic
or hyperbolic).
(ii) Change the principal part of the above equation to a canonical form (i.e.
without cross-derivatives).
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