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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 , x0, i.e. to find the kernel function p(t,x,y), such that u(x,t)= 0 ϕ(y)p(t,x,y)dy is a solution of the relevant Cauchy problem with u(x,0)=ϕ(x).
MSC:
35A30Geometric theory for PDE, characteristics, transformations
35K55Nonlinear parabolic equations
58J70Invariance and symmetry properties
35K65Parabolic equations of degenerate type
35A08Fundamental solutions of PDE