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Results tagged with linear-pde
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user 48757
Questions about linear partial differential equations. Often used in combination with the top-level tag ap.analysis-of-pdes.
2
votes
1
answer
344
views
Heat transfer: boundary conditions with fluid velocity
The following equation is considered:
$$
\frac{\partial u}{\partial t} - a\Delta u + \mathbf v \cdot \nabla u = f.
$$
I have difficulties in formulating boundary conditions for this equation.
If $\mat …
- 243
1
vote
1
answer
354
views
Existence of the solution of a linear parabolic pde
Good day!
Let $V = H^1(\Omega)$, $\Omega \subset \mathbb R^3$.
Consider the linear parabolic equation $y' + Ay = f$ where $f \in L^q(0,T;V')$, $y \in W = \{y \in L^p(0,T;V) \colon dy/dt \in L^q(0,T; …
- 243