# Questions tagged [linear-pde]

Questions about linear partial differential equations. Often used in combination with the top-level tag ap.analysis-of-pdes.

371 questions
Filter by
Sorted by
Tagged with
115 views

• 505
439 views

### Generalized Fuchsian-type PDE

Consider $$\big(1+ t\partial_t\big) \left(\partial^3_x+ {6\over x}\partial^2_x + {6\over x^2}\partial_x\right)A(x,t)+ {t\over (1-x)^3} A(x,t)=0$$ with the initial condition $A(x,0)=1$. In a small $t$...
• 141
164 views

• 185
59 views

### Geometric properties of the unique solution of an elliptic BVP involving the Lie derivative of the metric by a vector field

Setting Let $(M,g)$ be a compact Riemannian manifold with smooth boundary, and let $\nabla$ be its associated Levi-Civita connection. Consider the following formally self-adjoint, second order linear ...
• 808
1 vote
35 views

### Studying the evolution of laplacian in NS equation

The Navier-Stokes equation in $\mathbb{R}^3$ subjected to no gravitational forces are provided by: \label{Eq1} \dfrac{\partial }{\partial t} \textbf{u} + \left(\textbf{u}\cdot \nabla \...
• 305
1 vote
38 views

### Mixed boundary condition of parabolic equations

Let $\Omega$ be a bounded and smooth domain in $\mathbb{R}^n$. Assume that $$\partial\Omega=\partial\Omega_D\cup\partial\Omega_N,$$ where $\partial\Omega_D$ and $\partial\Omega_N$ are ...
• 1,155
47 views

• 123