Existence and Uniqueness of a Solution in the Space of BV Functions to the Equation of a Vibrating Membrane with a “Viscosity” Term

الملخص EN

A nonlinear equation of motion of vibrating membrane with a “viscosity” term is investigated.

Usually, the term -Δut is added, and it is well known that this equation is well posed in the space of W1,2 functions.

In this paper, the viscosity term is changed to -(div(∇u/1+|∇u|2))t, and it is proved that if initial data is slightly smooth (but belonging to W2,2 is sufficient), then a weak solution exists uniquely in the space of BV functions.