Conservation laws for equations of mixed elliptic-hyperbolic and degenerate types
For the Tricomi type equation \[ K(y) \Delta_x u + u_{yy} + f(u) = 0, \tag \(*\) \] where \((x,y)\in \mathbb R^N\times \mathbb R,\) \(N\geq 1,\) \(yK(y)>0,\) \(K(0)=0,\) the basic changes of basis of independent variables such as translation, rotation, dilation and inversion is considered. For these cases the conservation laws are founded. The uniqueness theorem for the Tricomi problem for equation \((*)\) in a star-like domain \(\Omega\) with \(N=2,\) \(f(u) = C u | u| ^{p},\) is proved with the help of symmetry groups.
scientific article; zbMATH DE number 2174751
scientific article