\(Q\)-conditional symmetry of the nonlinear \((1+2)\)--dimensional reaction-diffusion equations
The author deals with a study of a class of \((1+2)\)-dimensional nonlinear reaction-diffusion equations NEWLINE\[NEWLINE H(u) u_0 + \Delta u = F(u), \tag{1} NEWLINE\]NEWLINE where \(u = u(x) \in \mathbb{R}^1\), \(x=(x_0, \vec x)\), \(\vec x \in \mathbb{R}^2\); \( H(u)\), \(F(u)\) are arbitrary smooth functions. She presents a complete description of \(Q\)-conditional invariant operators for the equations (1). The obtained symmetries are used for finding exact solutions of the equations under consideration and reduction of the equations to ordinary differential equations.
scientific article; zbMATH DE number 6212598