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Results tagged with ap.analysis-of-pdes
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user 44079
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
3
votes
4
answers
502
views
Showing coercivity condition for an energy functional
Consider the energy functional $e(\cdot)$
\begin{align*}
e(f,Q)&=\int_a^b \bigg\{f^4\bigg[1+\|\frac{d}{dr}Q\|^2+f^2\dot f^2\bigg]\bigg\} \,dr,
\end{align*}
over the space of
\begin{equation*}
{\mat …
0
votes
Showing coercivity condition for an energy functional
The Euler-Lagrange Equations of the $e(f, Q)$ over the admissible space $\mathcal E$ arise as the following system
\begin{align*}
\left \{ \begin {array}{ll}
(i)\ \ \frac{d}{dr} \bigg[ f^4 Q^t \frac{ …
- 51