Self-Similar Solutions of a Convection Diffusion Equation And Related Semilinear Elliptic Problems
Julián Aguirre, Miguel Escobedo, Enrique Zuazua · Communications in Partial Differential Equations · 1990
We show that for each M>o, and locally Lipschitz function the elliptic equation: in RN has a positive and exponentially decaying solution with If Ψ is the solution is unique and strictly positive, and if Ψ is the solution is also . Because of the nonvariational nature of the elliptic problem, we use a topological degree argument. The existence of a family of positive self-similar solutions of the parabolic equation in x RN with follows. They are “source-type” solutions of the convection-diffusion equation above.