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Symmetry group methods for fundamental solutions. (English) Zbl 1065.35016
The authors use Lie symmetry group methods to find fundamental solutions for a class of partial differential equations of the form $u_t=xu_{xx}+f(x)u_x$, $x\geq 0$, i.e. to find the kernel function $p(t,x,y)$, such that $u(x,t)=\int_0^\infty\varphi(y)p(t,x,y)\,dy$ is a solution of the relevant Cauchy problem with $u(x,0)=\varphi(x)$.

35A30Geometric theory for PDE, characteristics, transformations
35K55Nonlinear parabolic equations
58J70Invariance and symmetry properties
35K65Parabolic equations of degenerate type
35A08Fundamental solutions of PDE
Full Text: DOI
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