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Let and be the Gauss-Weierstrass kernel.Consider the one dimensional heat equation on coupled with the initial condition.Which of the following is the unique solution of this IVP?

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MCQs on Partial Differential Equations.


Let<br><img src='https://www.fatskills.com/images2/GradExams/12A7E4C9-F7EB-4C75-8D54-50028A404713.png' height='22' width='84'/> and<br><img src='https://www.fatskills.com/images2/GradExams/918D150D-2105-46B8-A0CE-1E9CE158372B.png' height='20' width='240'/> be the Gauss-Weierstrass kernel.Consider the one dimensional heat equation<br><img src='https://www.fatskills.com/images2/GradExams/250820DE-BEC1-4CA8-996B-09EDB0F045B5.png' height='22' width='84'/> on<br><img src='https://www.fatskills.com/images2/GradExams/610DF5CE-623A-491E-AE7A-CF9808327AB7.png' height='14' width='14'/> coupled with the initial condition<br><img src='https://www.fatskills.com/images2/GradExams/0AFDDC6B-07EA-4186-9188-A6BB6AB7D405.png' height='20' width='178'/>.Which of the following is the unique solution of this IVP?





 
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