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Results tagged with ap.analysis-of-pdes
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user 57571
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
0
votes
1
answer
99
views
Existence and estimates of a solution of a perturbed first order partial differential equation
My question is as follows: Let $A=\partial_x-\frac y2\partial_z$, $B=\partial_y+\frac x2\partial_z$, and $\Omega\subset \mathbb R^3$ be a smooth bounded open set. Take $g\in C^\infty(\Omega)$ (if you …
- 277
5
votes
0
answers
96
views
Explicit fundamental solution of a class of hypoelliptic operators
Good evening,
my question is as follows:
Suppose we are given an operator $$L=a_1x_n\partial_{x_1}+\dotso+a_{n-1}x_n^{n-1}\partial_{x_{n-1}}+\partial_{x_n}^2,$$ for some nonzero constants $a_1,\dots …
- 277
4
votes
2
answers
2k
views
System of linear first order PDE with constant coefficients
recently in my researches I've come across the following operator
$$L\left(\begin{array}{c}
a_1\\
\vdots\\
a_n
\end{array}\right)=M_1\left(\begin{array}{c}
…
- 277
0
votes
1
answer
90
views
Boundary behaviour of a second order pde with characteristics
Good morning everybody. My question is inspired from the following fact:
Consider $\mathbb R^3$ endowed with coordinates $(x,y,z)$. Of course if we were to solve the second order pde $\partial_x^2 g( …
- 277
1
vote
1
answer
439
views
Cauchy problem for an overdetermined system of PDE
This question is strictly related to this one. Let us consider the differential system with constant coefficients
$$\left(\begin{array}{ccc}
B_{11} & B_{12} & 0\\
…
- 277