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Tagged with ap.analysis-of-pdes linear-pde
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Why is it impossible to reduce a linear PDE of the second order in more than two independent variables to canonical form globally
It is known that in the case of more than two independent variables, it is usually not possible (especially in the case of PDE with the variable coefficients) to reduce a linear partial differential ...
- 133
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Solvable PDEs and their Green's functions
I have a class of PDEs of the form
$$
-\Box\phi(x)+\lambda\phi_0^2(x)\phi(x)=0
$$
with $\phi_0^2(x)=\sum_{n=-\infty}^\infty b_ne^{ip_n\cdot x}$. I know some exact solutions for them (see here and ...
- 1,687
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characteristic surface
Hello,
I have the following 4 PDEs which I am trying to solve for $G(x,y,z)$ :
(1) $G_{xy}=0$
(2) $G_{xz}=0$
(3) $G_{yz}=0$
(4) $G_{xx}-G_{yy}=0$.
It is not hard to see that the general ...