Mixing
Stability of an elliptic PDE
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I'm reading An introduction to semilinear elliptic equations of Thierry Cazenave. In the middle of the text, he asserts that in general the groundstate solution (that is, the minimal solution with respect to an energy fucntional) is stable in some sense. However, he don't define what stable in this context means.
If someone can give me the definition of stability in the sense of an elliptic PDE, explain the reason for what groundstate solutions are stable in general and suggest some textbooks which introduce this subject, I will really appreciate.
pde stability-theory elliptic-operators
asked Jan 28 at 23:40
BBVMBBVM
18312
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I'm reading An introduction to semilinear elliptic equations of Thierry Cazenave. In the middle of the text, he asserts that in general the groundstate solution (that is, the minimal solution with respect to an energy fucntional) is stable in some sense. However, he don't define what stable in this context means.
If someone can give me the definition of stability in the sense of an elliptic PDE, explain the reason for what groundstate solutions are stable in general and suggest some textbooks which introduce this subject, I will really appreciate.
pde stability-theory elliptic-operators
asked Jan 28 at 23:40
BBVMBBVM
18312
$endgroup$
$begingroup$
Stability usually means that the solution doesn't change much when you change the initial data. If a system is unstable, then a small change to your initial data can severely impact the solution of your system. Suppose you are tasked with finding the initial data for a system. Then stability of a system guarantees that even if the initial data is imperfect, your solution will still be ``good enough''.
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– Quoka
Jan 30 at 19:19
add a comment |
$begingroup$
I'm reading An introduction to semilinear elliptic equations of Thierry Cazenave. In the middle of the text, he asserts that in general the groundstate solution (that is, the minimal solution with respect to an energy fucntional) is stable in some sense. However, he don't define what stable in this context means.
If someone can give me the definition of stability in the sense of an elliptic PDE, explain the reason for what groundstate solutions are stable in general and suggest some textbooks which introduce this subject, I will really appreciate.
pde stability-theory elliptic-operators
asked Jan 28 at 23:40
BBVMBBVM
18312
$endgroup$
I'm reading An introduction to semilinear elliptic equations of Thierry Cazenave. In the middle of the text, he asserts that in general the groundstate solution (that is, the minimal solution with respect to an energy fucntional) is stable in some sense. However, he don't define what stable in this context means.
If someone can give me the definition of stability in the sense of an elliptic PDE, explain the reason for what groundstate solutions are stable in general and suggest some textbooks which introduce this subject, I will really appreciate.
pde stability-theory elliptic-operators
pde stability-theory elliptic-operators
asked Jan 28 at 23:40
BBVMBBVM
18312
asked Jan 28 at 23:40
BBVMBBVM
18312
asked Jan 28 at 23:40
BBVMBBVM
18312
asked Jan 28 at 23:40
BBVMBBVM
18312
asked Jan 28 at 23:40
BBVMBBVM
18312
18312
$begingroup$
Stability usually means that the solution doesn't change much when you change the initial data. If a system is unstable, then a small change to your initial data can severely impact the solution of your system. Suppose you are tasked with finding the initial data for a system. Then stability of a system guarantees that even if the initial data is imperfect, your solution will still be ``good enough''.
$endgroup$
– Quoka
Jan 30 at 19:19
add a comment |
$begingroup$
Stability usually means that the solution doesn't change much when you change the initial data. If a system is unstable, then a small change to your initial data can severely impact the solution of your system. Suppose you are tasked with finding the initial data for a system. Then stability of a system guarantees that even if the initial data is imperfect, your solution will still be ``good enough''.
$endgroup$
– Quoka
Jan 30 at 19:19
$begingroup$
Stability usually means that the solution doesn't change much when you change the initial data. If a system is unstable, then a small change to your initial data can severely impact the solution of your system. Suppose you are tasked with finding the initial data for a system. Then stability of a system guarantees that even if the initial data is imperfect, your solution will still be ``good enough''.
$endgroup$
– Quoka
Jan 30 at 19:19
$begingroup$
Stability usually means that the solution doesn't change much when you change the initial data. If a system is unstable, then a small change to your initial data can severely impact the solution of your system. Suppose you are tasked with finding the initial data for a system. Then stability of a system guarantees that even if the initial data is imperfect, your solution will still be ``good enough''.
$endgroup$
– Quoka
Jan 30 at 19:19
add a comment |
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$begingroup$
Stability usually means that the solution doesn't change much when you change the initial data. If a system is unstable, then a small change to your initial data can severely impact the solution of your system. Suppose you are tasked with finding the initial data for a system. Then stability of a system guarantees that even if the initial data is imperfect, your solution will still be ``good enough''.
$endgroup$
– Quoka
Jan 30 at 19:19