Mixing
PDE - Wave Equation With More Than Two Variables
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Solve the PDE:
$$Delta U = U_{tt}$$
BC: $$U(R) = 0$$
$$U (0) = 0$$
My professor had this PDE problem on the board. I try to read my textbook "Solution Techniques for Elementary Partial Differential Equation," but I could not find something similar. I understand it as the functions/values of the boundary and the origin are both zero.
Hint: Because $U(0)=0$, this PDE has many solutions.
pde
asked 2 days ago
mathmajor
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up vote
0
down vote
favorite
Solve the PDE:
$$Delta U = U_{tt}$$
BC: $$U(R) = 0$$
$$U (0) = 0$$
My professor had this PDE problem on the board. I try to read my textbook "Solution Techniques for Elementary Partial Differential Equation," but I could not find something similar. I understand it as the functions/values of the boundary and the origin are both zero.
Hint: Because $U(0)=0$, this PDE has many solutions.
pde
asked 2 days ago
mathmajor
1
New contributor
mathmajor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
@FelixMarin I didn't see you change your comment. Yeah, in the title I said it has more than two variables.
– mathmajor
2 days ago
Sorry. I didn't read the title. I just deleted my previous comment.
– Felix Marin
2 days ago
The solution is in the form of Bessel functions of the first kind. See here for a guide: math.upenn.edu/~deturck/m241/wavedisk.pdf. The condition at the origin only excludes $J_0$ as a solution; higher-order Bessel functions are still valid.
– Dylan
yesterday
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Solve the PDE:
$$Delta U = U_{tt}$$
BC: $$U(R) = 0$$
$$U (0) = 0$$
My professor had this PDE problem on the board. I try to read my textbook "Solution Techniques for Elementary Partial Differential Equation," but I could not find something similar. I understand it as the functions/values of the boundary and the origin are both zero.
Hint: Because $U(0)=0$, this PDE has many solutions.
pde
asked 2 days ago
mathmajor
1
New contributor
mathmajor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Solve the PDE:
$$Delta U = U_{tt}$$
BC: $$U(R) = 0$$
$$U (0) = 0$$
My professor had this PDE problem on the board. I try to read my textbook "Solution Techniques for Elementary Partial Differential Equation," but I could not find something similar. I understand it as the functions/values of the boundary and the origin are both zero.
Hint: Because $U(0)=0$, this PDE has many solutions.
pde
pde
asked 2 days ago
mathmajor
1
New contributor
mathmajor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
mathmajor
1
New contributor
mathmajor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
mathmajor
1
New contributor
mathmajor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
mathmajor
1
asked 2 days ago
mathmajor
1
1
New contributor
mathmajor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
mathmajor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
mathmajor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
@FelixMarin I didn't see you change your comment. Yeah, in the title I said it has more than two variables.
– mathmajor
2 days ago
Sorry. I didn't read the title. I just deleted my previous comment.
– Felix Marin
2 days ago
The solution is in the form of Bessel functions of the first kind. See here for a guide: math.upenn.edu/~deturck/m241/wavedisk.pdf. The condition at the origin only excludes $J_0$ as a solution; higher-order Bessel functions are still valid.
– Dylan
yesterday
add a comment |
@FelixMarin I didn't see you change your comment. Yeah, in the title I said it has more than two variables.
– mathmajor
2 days ago
Sorry. I didn't read the title. I just deleted my previous comment.
– Felix Marin
2 days ago
The solution is in the form of Bessel functions of the first kind. See here for a guide: math.upenn.edu/~deturck/m241/wavedisk.pdf. The condition at the origin only excludes $J_0$ as a solution; higher-order Bessel functions are still valid.
– Dylan
yesterday
@FelixMarin I didn't see you change your comment. Yeah, in the title I said it has more than two variables.
– mathmajor
2 days ago
@FelixMarin I didn't see you change your comment. Yeah, in the title I said it has more than two variables.
– mathmajor
2 days ago
Sorry. I didn't read the title. I just deleted my previous comment.
– Felix Marin
2 days ago
Sorry. I didn't read the title. I just deleted my previous comment.
– Felix Marin
2 days ago
The solution is in the form of Bessel functions of the first kind. See here for a guide: math.upenn.edu/~deturck/m241/wavedisk.pdf. The condition at the origin only excludes $J_0$ as a solution; higher-order Bessel functions are still valid.
– Dylan
yesterday
The solution is in the form of Bessel functions of the first kind. See here for a guide: math.upenn.edu/~deturck/m241/wavedisk.pdf. The condition at the origin only excludes $J_0$ as a solution; higher-order Bessel functions are still valid.
– Dylan
yesterday
add a comment |
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mathmajor is a new contributor. Be nice, and check out our Code of Conduct.
mathmajor is a new contributor. Be nice, and check out our Code of Conduct.
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@FelixMarin I didn't see you change your comment. Yeah, in the title I said it has more than two variables.
– mathmajor
2 days ago
Sorry. I didn't read the title. I just deleted my previous comment.
– Felix Marin
2 days ago
The solution is in the form of Bessel functions of the first kind. See here for a guide: math.upenn.edu/~deturck/m241/wavedisk.pdf. The condition at the origin only excludes $J_0$ as a solution; higher-order Bessel functions are still valid.
– Dylan
yesterday