On a nonlinear parabolic problem arising in some models related to turbulent flows
SIAM Journal on Mathematical Analysis
Qualitative properties of the ice-thickness in a 3D model
WSEAS Transactions on Mathematics
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The paper is devoted to the study of the homogeneous Dirichlet problem for the doubly nonlinear parabolic equation with nonstandard growth conditions:u"t=diva(x,t,u)|u|^@a^(^x^,^t^)|@?u|^p^(^x^,^t^)^-^2@?u+f(x,t)with given variable exponents @a(x, t) and p(x, t). We establish conditions on the data which guarantee the existence of bounded weak solutions in suitable Sobolev-Orlicz spaces.