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

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19
votes
4answers
2k views

Classification of PDE

Recently I have been attending a course on PDE's. I was totally ignorant of the subject and wasn't that motivated to be honest. But I was intrigued and felt I had to take the course seriously both for ...
1
vote
3answers
455 views

How to prove/disprove that quasiconformal maps send measure-zero sets to measure-zero sets

$Qn#1 $ : Let $f:U\to V$ be a $K$ quasiconformal homeomorphism ( NOT diffeomorphism ) of plane open subsets of $C$. By my definition of quasiconformality, I mean 1)$f$ is continuous, 2)the weak ...
1
vote
2answers
268 views

Structure of solutions of a PDE from a game theory problem

I found the following the following differential equation in the context of a Game Theory problem. I was wondering if this is related to any known family of equations or whether there is any hint ...
2
votes
1answer
393 views

orthonormal basis of eigenvectors for laplacian on a concave polygon

I am interested in the Laplace operator $\Delta$ on a concave polygon. When the polygon is convex, it is known that $\Delta: H^2(\Omega) \rightarrow L^2(\Omega)$ is boundedly invertible. In addition, ...
6
votes
3answers
811 views

Analytical solution to a Linear advection-reaction PDE

I am looking for an analytical solution for the linear PDE $(1)\qquad\qquad \qquad f_t+ A f_x + B f = 0, $ Where $A$ and $B$ are constant matrices and $f=f(x,t)$ is a vector. Clearly each one of ...