Entire solutions of a variation of the eikonal equation and related PDEs
Feng Lü
Abstract
Abstract The aim of this paper is twofold. The first aim is to describe the entire solutions of the partial differential equation (PDE) $u_{z_1}^2+2Bu_{z_1}u_{z_2}+u_{z_2}^2=e^g$ , where B is a constant and g is a polynomial or an entire function in $\mathbb {C}^2$ . The second aim is to consider the entire solutions of another PDE, which is a generalization of the well-known PDE of tubular surfaces.
Topics & Concepts
Eikonal equationPartial differential equationGeneralizationMathematicsConstant (computer programming)Function (biology)PolynomialFirst-order partial differential equationMathematical analysisPartial derivativePure mathematicsComputer scienceEvolutionary biologyBiologyProgramming languageMeromorphic and Entire FunctionsAdvanced Differential Equations and Dynamical SystemsAlgebraic Geometry and Number Theory