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Let be a domain with piecewise smooth boundary and suppose that the continuously differentiable function satisfies the heat equation and is nontrivial on.Which of the following conditions might be true? I., for all. II., where is not identically zero on. III., for all.

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MCQs on Partial Differential Equations.


Let<br><img src='https://www.fatskills.com/images2/GradExams/20BEC897-C957-48AB-A852-6051036C72E2.png' height='18' width='66'/> be a domain with piecewise smooth boundary and suppose that the continuously differentiable function<br><img src='https://www.fatskills.com/images2/GradExams/2F0CF4F3-04C0-47C9-8876-D1B2BEB81CE6.png' height='20' width='168'/> satisfies the heat equation<br><img src='https://www.fatskills.com/images2/GradExams/F8F10519-9C39-4969-9353-77AED343CD6E.png' height='18' width='81'/> and is nontrivial on<br><img src='https://www.fatskills.com/images2/GradExams/E1E336DB-6F15-4579-89B8-FE039B799486.png' height='14' width='17'/>.Which of the following conditions might be true?<br/> I.<br><img src='https://www.fatskills.com/images2/GradExams/DDFF41B4-A7B1-495E-BADA-D609C3408D02.png' height='20' width='90'/>, for all<br><img src='https://www.fatskills.com/images2/GradExams/F7041EB9-B9DC-463E-BDFE-E49614465BC9.png' height='19' width='115'/>.<br/> II.<br><img src='https://www.fatskills.com/images2/GradExams/1A0A9A60-53C2-466A-A187-166DD8447546.png' height='20' width='119'/>, where<br><img src='https://www.fatskills.com/images2/GradExams/203085BB-4CDE-402E-A5EC-575C34B85EBF.png' height='18' width='10'/> is not identically zero on<br><img src='https://www.fatskills.com/images2/GradExams/E1E336DB-6F15-4579-89B8-FE039B799486.png' height='14' width='17'/>.<br/> III.<br><img src='https://www.fatskills.com/images2/GradExams/190827CE-6E74-4D39-8C09-CDFF298818B9.png' height='20' width='111'/>, for all<br><img src='https://www.fatskills.com/images2/GradExams/F7041EB9-B9DC-463E-BDFE-E49614465BC9.png' height='19' width='115'/>.






 
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