On the formation of singularities in the linear advection-diffusion equation with a redefinition of the boundary condition
Abstract
We study finite-time singularities in the linear advection–diffusion equation with a variable speed on a semi-infinite line. The variable speed is determined by an additional condition at the boundary, which models the dynamics of a contact line of a hydrodynamic flow at a 180◦ contact angle. Using apriori energy estimates, we derive conditions on variable speed that guarantee that a sufficiently smooth solution of the linear advection–diffusion equation blows up in a finite time. Using the class of self-similar solutions to the linear advection–diffusion equation, we find the blow-up rate of singularity formation. This blow-up rate does not agree with previous numerical simulations of the model problem.
About the Authors
D. . Pelinovsky
Alexeev Nizhny Novgorod State Technical University; McMaster University Hamilton, Ontario, Canada
Russian Federation
Russian Federation
A. . Giniyatullin
Alexeev Nizhny Novgorod State Technical University
Russian Federation
Russian Federation
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