Solve the PDE $x^2U_{xx}+U_{yy}+Ulog U=0$
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1
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Solve the PDE $x^2U_{xx}+U_{yy}+Ulog U=0$
my attempt:
this is elliptic and $lambda=pm frac{i}{x}$
so $frac{dy}{dx}=frac{i}{x}, frac{dy}{dx}=frac{-i}{x}$
from here to how to processed
pde
asked Nov 23 at 5:19
learner
997
add a comment |
up vote
1
down vote
favorite
1
Solve the PDE $x^2U_{xx}+U_{yy}+Ulog U=0$
my attempt:
this is elliptic and $lambda=pm frac{i}{x}$
so $frac{dy}{dx}=frac{i}{x}, frac{dy}{dx}=frac{-i}{x}$
from here to how to processed
pde
asked Nov 23 at 5:19
learner
997
I guess you mean $$x^{2} U_{xx} + color{red}{U}_{yy} + U log U = 0$$
– Mattos
Nov 23 at 6:07
What are the boundary and/or initial conditions for the PDE?
– DavidG
Nov 23 at 6:18
Also, are you only seeking an analytic solution? or will you also employ Numerical Methods?
– DavidG
Nov 23 at 6:19
@DavidG..trying to find with charctertic curves method
– learner
Nov 23 at 6:22
Separation of variables yields begin{align} x^{2}X'' + X log X &= - lambda X \ Y'' + Y log Y &= lambda Y end{align} where the separation constant is $-lambda$. However, as DavidG highlighted, you haven't specified any data with your PDE so we don't know whether this is a reasonable ansatz.
– Mattos
Nov 24 at 1:00
add a comment |
up vote
1
down vote
favorite
1
up vote
1
down vote
favorite
1
1
Solve the PDE $x^2U_{xx}+U_{yy}+Ulog U=0$
my attempt:
this is elliptic and $lambda=pm frac{i}{x}$
so $frac{dy}{dx}=frac{i}{x}, frac{dy}{dx}=frac{-i}{x}$
from here to how to processed
pde
asked Nov 23 at 5:19
learner
997
Solve the PDE $x^2U_{xx}+U_{yy}+Ulog U=0$
my attempt:
this is elliptic and $lambda=pm frac{i}{x}$
so $frac{dy}{dx}=frac{i}{x}, frac{dy}{dx}=frac{-i}{x}$
from here to how to processed
pde
pde
asked Nov 23 at 5:19
learner
997
asked Nov 23 at 5:19
learner
997
edited Nov 23 at 6:08
asked Nov 23 at 5:19
learner
997
asked Nov 23 at 5:19
learner
997
asked Nov 23 at 5:19
learner
997
997
I guess you mean $$x^{2} U_{xx} + color{red}{U}_{yy} + U log U = 0$$
– Mattos
Nov 23 at 6:07
What are the boundary and/or initial conditions for the PDE?
– DavidG
Nov 23 at 6:18
Also, are you only seeking an analytic solution? or will you also employ Numerical Methods?
– DavidG
Nov 23 at 6:19
@DavidG..trying to find with charctertic curves method
– learner
Nov 23 at 6:22
Separation of variables yields begin{align} x^{2}X'' + X log X &= - lambda X \ Y'' + Y log Y &= lambda Y end{align} where the separation constant is $-lambda$. However, as DavidG highlighted, you haven't specified any data with your PDE so we don't know whether this is a reasonable ansatz.
– Mattos
Nov 24 at 1:00
add a comment |
I guess you mean $$x^{2} U_{xx} + color{red}{U}_{yy} + U log U = 0$$
– Mattos
Nov 23 at 6:07
What are the boundary and/or initial conditions for the PDE?
– DavidG
Nov 23 at 6:18
Also, are you only seeking an analytic solution? or will you also employ Numerical Methods?
– DavidG
Nov 23 at 6:19
@DavidG..trying to find with charctertic curves method
– learner
Nov 23 at 6:22
Separation of variables yields begin{align} x^{2}X'' + X log X &= - lambda X \ Y'' + Y log Y &= lambda Y end{align} where the separation constant is $-lambda$. However, as DavidG highlighted, you haven't specified any data with your PDE so we don't know whether this is a reasonable ansatz.
– Mattos
Nov 24 at 1:00
I guess you mean $$x^{2} U_{xx} + color{red}{U}_{yy} + U log U = 0$$
– Mattos
Nov 23 at 6:07
I guess you mean $$x^{2} U_{xx} + color{red}{U}_{yy} + U log U = 0$$
– Mattos
Nov 23 at 6:07
What are the boundary and/or initial conditions for the PDE?
– DavidG
Nov 23 at 6:18
What are the boundary and/or initial conditions for the PDE?
– DavidG
Nov 23 at 6:18
Also, are you only seeking an analytic solution? or will you also employ Numerical Methods?
– DavidG
Nov 23 at 6:19
Also, are you only seeking an analytic solution? or will you also employ Numerical Methods?
– DavidG
Nov 23 at 6:19
@DavidG..trying to find with charctertic curves method
– learner
Nov 23 at 6:22
@DavidG..trying to find with charctertic curves method
– learner
Nov 23 at 6:22
Separation of variables yields begin{align} x^{2}X'' + X log X &= - lambda X \ Y'' + Y log Y &= lambda Y end{align} where the separation constant is $-lambda$. However, as DavidG highlighted, you haven't specified any data with your PDE so we don't know whether this is a reasonable ansatz.
– Mattos
Nov 24 at 1:00
Separation of variables yields begin{align} x^{2}X'' + X log X &= - lambda X \ Y'' + Y log Y &= lambda Y end{align} where the separation constant is $-lambda$. However, as DavidG highlighted, you haven't specified any data with your PDE so we don't know whether this is a reasonable ansatz.
– Mattos
Nov 24 at 1:00
add a comment |
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I guess you mean $$x^{2} U_{xx} + color{red}{U}_{yy} + U log U = 0$$
– Mattos
Nov 23 at 6:07
What are the boundary and/or initial conditions for the PDE?
– DavidG
Nov 23 at 6:18
Also, are you only seeking an analytic solution? or will you also employ Numerical Methods?
– DavidG
Nov 23 at 6:19
@DavidG..trying to find with charctertic curves method
– learner
Nov 23 at 6:22
Separation of variables yields begin{align} x^{2}X'' + X log X &= - lambda X \ Y'' + Y log Y &= lambda Y end{align} where the separation constant is $-lambda$. However, as DavidG highlighted, you haven't specified any data with your PDE so we don't know whether this is a reasonable ansatz.
– Mattos
Nov 24 at 1:00