Dependency of the Solution of a Class of Quartic Partial Differential Quasilinear Equation With Periodic Boundary Condition on varepsilon

In this paper, we study the multidimensional mixed problem with periodic boundary condition for quasilinear Euler-Bernoulli equation fracpartial^2 upartial t^2-varepsilon b^2 fracpartial^4 upartial t^2partial x^2+a^2fracpartial^4 upartial x^4= f(t,x,u). We also consider the mixed problem fracpartial^2 upartial t^2+a^2 fracpartial^4 vpartial x^4= f(t,x,v). Finally we prove that the solution function u(t,x,\varepsilon) of the quasilinear Euler-Bernoulli equation is convergent to the solution function v(t,x) of the quasilinear quartic equation, as varepsilon rightarrow0.