ON SOLVABILITY OF MODEL NONHOMOGENEOUS PROBLEMS FOR SEMILINEAR PARABOLIC EQUATIONS WITH VARIABLE EXPONENTS OF NONLINEARITY

Анотація

The nonhomogeneous initial-boundary value Dirichlet problem for the equation

$u_t-\Delta u+g(x,t){\left|u\right|}^{q(x,t)-2}u=f(x,y)$

in cylinder domain is considered. If the condition $1<q_0\le q(x,t)\le q^0<2$ is satisfied, then the existence of the mild solution of this problem is proved.