On Singular Semilinear Elliptic Equations
Technical rept. Oct 90-Apr 91,
NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF MATHEMATICS
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We study the singular semilinear elliptic equation. This type of equation arises in the boundary layer theory of viscous fluids. From the results it follows that the equation has a unique classical solution within a bounded domain omega, where px is a sufficiently regular function which is positive on omega. Kusano and Swanson gave the existence proof on exterior domains. In this paper we show via the upper and lower solution method, which is also referred to as the barrier method, that the equation has a bounded positive entire solution vanishing at infinity. It is observed by Callegari, Friedman and Nachman that if the partial differential equations describing the boundary layer behind a rarefaction or shock wave with viscosity proportional to the temperature traveling down, and perpendicular to, a flat plate are written in terms of a stream function and a similarity variable the following Blasius-type equation emerges.
- Numerical Mathematics