Equação ao de Kirchhoff fracamente dissipativa: existência, unicidade e decaimento exponencial

Abstract

This academic production we will prove the existence and uniqueness of the strong solution of the Cauchy problem in L2(Ω) whose partial differential equation is given by d2u/dt2(x, t) − M(∥∇u(x, t)∥2)∆u(x, t) + δdu/dt (x, t) = 0 u(x, t) = 0 em Γ × [0, T[ u(x, 0) = u0(x) em Ω du/dt (x, 0) = u1(x) em Ω where δ is a small positive constant, M(s) is a function of class C1 , Ω is an open bounded

one with boundary Γ.Furthermore, we will demonstrate the exponential decay of the solution to the above problem.