BLOW-UP ANALYSIS FOR A CLASS OF PLATE VISCOELASTIC p(x) TYPE INVERSE SOURCE PROBLEM WITH VARIABLE-EXPONENT NONLINEARITIES

In this work, we study the blow-up analysis for a class of plate viscoelastic p(x)-Kirchhoff type inverse source problem of the form: utt + Delta(2) u -( alpha + b integral(Omega) 1/p(x) vertical bar del u vertical bar(p(x)) dx ) Delta p(x)u - integral(t)(0) g(t - tau)Delta(2) u(tau)d tau Under suitable conditions on kernel of the memory, initial data and variable exponents, we prove the blow up of solutions in two cases: linear damping term (m(x) equivalent to 2) and nonlinear damping term (m(x) > 2). Precisely, we show that the solutions with positive initial energy blow up in a finite time when m(x) equivalent to 2 and blow up at infinity if m(x) > 2