PDE $\partial_t f(x,y,t)=cy (\partial_xf)+3x\partial_y(yf)+\frac{1}{2}c^2y^2(\partial_{xx}f) \\$

Asked May 24 '22 at 22:53

Active May 24 '22 at 22:53

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I have the following PDE

$\partial_t f(x,y,t)=cy (\partial_xf)+3x\partial_y(yf)+\frac{1}{2}c^2y^2(\partial_{xx}f) \\$

where $c \in \mathbb{R}$

I would like to know what type of PDE is, any information about it, and its possible solutions given an initial condition. In particular, I would like to know if every term on the right side forms a generator of a $C_0$ semigroup.

asked May 24 '22 at 22:53

Asanovic Tomas

1

Can you share some details about the origin of this PDE? The origin may help others search on the basis of the origin (e.g. physics , optics etc.). – Sarvesh Ravichandran Iyer May 25 '22 at 04:32

PDE $\partial_t f(x,y,t)=cy (\partial_xf)+3x\partial_y(yf)+\frac{1}{2}c^2y^2(\partial_{xx}f) \\$

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