A well posedness result for nonlinear viscoelastic equations with memory

作者：Conti Monica; Marchini Elsa M; Pata Vittorino^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2014, 94: 206-216.

DOI：10.1016/j.na.2013.08.015

• Nonlinear viscoelastic equations
• Memory kernel
• Existence of solutions
• Uniqueness
• Continuous dependence

We establish an existence, uniqueness and continuous dependence result for the weak solutions to the nonlinear viscoelastic equation with hereditary memory on a bounded three-dimensional domain
vertical bar partial derivative(t)u vertical bar(rho)partial derivative(tt)u - Delta partial derivative(tt)u + gamma(-Delta)(theta)partial derivative(t)u -alpha Delta u + integral(infinity)(0)mu(s)Delta u(t - s)ds + f (u) = h
with Dirichlet boundary conditions.

• 出版日期2014-1