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Results tagged with ap.analysis-of-pdes
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user 132487
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
1
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0
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76
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While doing Lp estimates, is the constant C monotonically increasing with respect to the par...
For example, consider the third boundary value problem:
\begin{align}
&\frac{\partial u}{\partial t}-\sum_{i,j=1}^n a_{ij}(x,t) \frac{\partial^2 u}{\partial x_i \partial x_j} + \sum_{i=1}^n b_i(x, …
- 51
1
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Are there maximum principles related to the third boundary condition?
I am working on this problem
\begin{equation}
\begin{cases}
u''(s)+\frac{2}{s} u'(s)=R^2 f(u) \quad \text{ for } \eta<s<1, \\
u'(\eta)=0, \ u'(1)+\beta R (u(1)-\bar{\sigma})=0,
\end{cases}
\end{equati …
- 51
0
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Does the function with the αth-weak partial derivative has the βth-weak partial derivative w...
The definition of weak derivative in the book Partial Differential Equations by Evans is stated as follows:
Suppose $u,v \in L_{loc}^1(U)$, and $\alpha$ is a multiindex. We say that $v$ is the $\a …
- 51