Existence Result to a Class of Parabolic Equations with Nonstandard Growth Condition and Zero Order Term

Abstract:

      In the setting of variable exponent, an existence result to a class of parabolic equations with zero order term is proved. The proof of existence relies essentially on selecting some suitable test functions based upon the integrability of the source term and the zero order term simultaneously. By virtue of a priori estimates and some limit analyses, the weak limit of the nonlinear principal term is identified via the Young measures method.