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Results tagged with linear-pde
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user 533903
Questions about linear partial differential equations. Often used in combination with the top-level tag ap.analysis-of-pdes.
1
vote
0
answers
5
views
Uniform bound on the first moment for a perturbed advection-diffusion equation
I am studying the solution $u = u(t,x)$ to the following problem on the positive half-line:
$$
\begin{cases}
u_t = u_{xx} + u_x - \frac{1}{1+t}(xu)_x, & \quad t > 0, \, x > 0, \\[2mm]
-u_x = u , & \qu …
- 43
3
votes
1
answer
70
views
$L^{1}$-convergence to steady states for an advection-diffusion equation on the half real line
I consider the following problem on the half real line
$$
\begin{cases}
u_t = u_{xx} + u_x, & \quad t > 0, \, x > 0, \\[2mm]
-u_x|_{x=0} = u|_{x=0}, & \quad t > 0, \, x = 0, \\[2mm]
u|_{t=0} = u_0, & …
- 43