GATE MA topic:partial-differential-equations PYQs & Answers

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topic:partial-differential-equations

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Questions 1–10 of 39. Imported answers require independent review unless marked reviewed.

Topic practice 39 questionsPage 1 of 4

Let

be the solution of the initial value problem for the heat equation on the real line:

with the initial condition

is the Fourier transform of

with respect to

, then

is equal to

Your answerChoose one option.

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Consider the following partial differential equation:

where

and

are distinct positive real numbers. The combination(s) of the values of the real parameters

and

for which

is a solution of the given partial differential equation, is/are

Your answerSelect all correct options. You can choose more than one.

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Let

satisfy the wave equation

, with

and

. By using D’Alembert’s formula, the maximum value of

for

Your answerChoose one option.

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Consider the Laplace equation

, with the boundary conditions

. Then the value of

is equal to

Your answerChoose one option.

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Let

be the open unit disc and

be its boundary. If

is the solution of the following Dirichlet problem

then the value of

is ________. (answer in integer)

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The partial differential equation

Your answerChoose one option.

elliptic in the region

hyperbolic in the region

elliptic in the region

hyperbolic in the region

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Let

be the solution of the following initial-boundary value problem

Then, for each

, the value of

Your answerChoose one option.

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Let

be the solution of the initial-value problem

. Then, the value of

Your answerChoose one option.

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Let

be the solution of the initial value problem

and let

be the solution of the initial value problem

Then, which of the following is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

for all

and for all

is not defined for certain values of

is not defined for any

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Let

be the solution of the initial-boundary value problem

Then, which of the following is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

for all

and

for all

and

is a decreasing function of

is not a decreasing function of

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GATE MA topic:partial-differential-equations PYQs

How to practice topic:partial-differential-equations

Question 15

Question 25

Question 43

Question 44

Question 61

Question 19

Question 20

Question 40

Question 51

Question 52