Mixing
the heat equation with solution-dependent coefficients
2
$begingroup$
I meet the problem
$$u_t(t,x)=frac{A}{B-u}u_{xx}(t,x)$$
with the boundary conditions:
$$u(0,x)=B, xin[0,H]$$ $$u(t,0)=u(t,H)=0, t>0$$ $$u(+infty,x)=0$$
I have not any idea to start. Can you help me please.
pde heat-equation
edited Jan 15 at 9:18
El borito
668216
asked Jan 15 at 8:51
Pham Van HienPham Van Hien
113
$endgroup$
add a comment |
2
$begingroup$
I meet the problem
$$u_t(t,x)=frac{A}{B-u}u_{xx}(t,x)$$
with the boundary conditions:
$$u(0,x)=B, xin[0,H]$$ $$u(t,0)=u(t,H)=0, t>0$$ $$u(+infty,x)=0$$
I have not any idea to start. Can you help me please.
pde heat-equation
edited Jan 15 at 9:18
El borito
668216
asked Jan 15 at 8:51
Pham Van HienPham Van Hien
113
$endgroup$
$begingroup$
This would be a good candidate for a Laplace tranform, however you may have a tricky inverse transform to deal with.
$endgroup$
– DaveNine
Jan 16 at 20:45
$begingroup$
Thanks for your answer, i will try.
$endgroup$
– Pham Van Hien
Jan 17 at 4:15
$begingroup$
Since this is nonlinear, and you’re considering an IVBP, there may not be an explicit solution anyways. Can you provide more background to the problem?
$endgroup$
– DaveNine
Jan 17 at 19:06
add a comment |
2
2
2
1
$begingroup$
I meet the problem
$$u_t(t,x)=frac{A}{B-u}u_{xx}(t,x)$$
with the boundary conditions:
$$u(0,x)=B, xin[0,H]$$ $$u(t,0)=u(t,H)=0, t>0$$ $$u(+infty,x)=0$$
I have not any idea to start. Can you help me please.
pde heat-equation
edited Jan 15 at 9:18
El borito
668216
asked Jan 15 at 8:51
Pham Van HienPham Van Hien
113
$endgroup$
I meet the problem
$$u_t(t,x)=frac{A}{B-u}u_{xx}(t,x)$$
with the boundary conditions:
$$u(0,x)=B, xin[0,H]$$ $$u(t,0)=u(t,H)=0, t>0$$ $$u(+infty,x)=0$$
I have not any idea to start. Can you help me please.
pde heat-equation
pde heat-equation
edited Jan 15 at 9:18
El borito
668216
asked Jan 15 at 8:51
Pham Van HienPham Van Hien
113
edited Jan 15 at 9:18
El borito
668216
asked Jan 15 at 8:51
Pham Van HienPham Van Hien
113
edited Jan 15 at 9:18
El borito
668216
edited Jan 15 at 9:18
El borito
668216
edited Jan 15 at 9:18
El borito
668216
668216
asked Jan 15 at 8:51
Pham Van HienPham Van Hien
113
asked Jan 15 at 8:51
Pham Van HienPham Van Hien
113
asked Jan 15 at 8:51
Pham Van HienPham Van Hien
113
113
$begingroup$
This would be a good candidate for a Laplace tranform, however you may have a tricky inverse transform to deal with.
$endgroup$
– DaveNine
Jan 16 at 20:45
$begingroup$
Thanks for your answer, i will try.
$endgroup$
– Pham Van Hien
Jan 17 at 4:15
$begingroup$
Since this is nonlinear, and you’re considering an IVBP, there may not be an explicit solution anyways. Can you provide more background to the problem?
$endgroup$
– DaveNine
Jan 17 at 19:06
add a comment |
$begingroup$
This would be a good candidate for a Laplace tranform, however you may have a tricky inverse transform to deal with.
$endgroup$
– DaveNine
Jan 16 at 20:45
$begingroup$
Thanks for your answer, i will try.
$endgroup$
– Pham Van Hien
Jan 17 at 4:15
$begingroup$
Since this is nonlinear, and you’re considering an IVBP, there may not be an explicit solution anyways. Can you provide more background to the problem?
$endgroup$
– DaveNine
Jan 17 at 19:06
$begingroup$
This would be a good candidate for a Laplace tranform, however you may have a tricky inverse transform to deal with.
$endgroup$
– DaveNine
Jan 16 at 20:45
$begingroup$
This would be a good candidate for a Laplace tranform, however you may have a tricky inverse transform to deal with.
$endgroup$
– DaveNine
Jan 16 at 20:45
$begingroup$
Thanks for your answer, i will try.
$endgroup$
– Pham Van Hien
Jan 17 at 4:15
$begingroup$
Thanks for your answer, i will try.
$endgroup$
– Pham Van Hien
Jan 17 at 4:15
$begingroup$
Since this is nonlinear, and you’re considering an IVBP, there may not be an explicit solution anyways. Can you provide more background to the problem?
$endgroup$
– DaveNine
Jan 17 at 19:06
$begingroup$
Since this is nonlinear, and you’re considering an IVBP, there may not be an explicit solution anyways. Can you provide more background to the problem?
$endgroup$
– DaveNine
Jan 17 at 19:06
add a comment |
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$begingroup$
This would be a good candidate for a Laplace tranform, however you may have a tricky inverse transform to deal with.
$endgroup$
– DaveNine
Jan 16 at 20:45
$begingroup$
Thanks for your answer, i will try.
$endgroup$
– Pham Van Hien
Jan 17 at 4:15
$begingroup$
Since this is nonlinear, and you’re considering an IVBP, there may not be an explicit solution anyways. Can you provide more background to the problem?
$endgroup$
– DaveNine
Jan 17 at 19:06