Stabilization of the solution of a doubly nonlinear parabolic equation

Existence of solution for parabolic equation with non-power nonlinearities

“…By direct calculations we find that Θ( ) = 1/30 , integral (10) diverges and * ( ) = ( /30) 30 . It is easy to check that these functions satisfy conditions (5), (7), (12)- (16) and Theorem 1 holds true.…”

“…In particular, as 0 = 0, we have (0, ) → 0 ( ) almost everywhere in Ω. In the next step we employ a lemma proven in [16].…”

“…The case of a power function ( ), ( ) = | | , was considered in work [16]. At that, as 2 and < 2, there were employed different techniques of passing to the limit in Galerkin's approximations.…”

“…It is easy to make sure that conditions (7), (12)- (16) are satisfied and Theorem 1 hold true. Despite of a long list of conditions in the Introduction, there is a wide class of equations satisfying these conditions.…”

Estimates of decay rate for solution to parabolic equation with non-power nonlinearities

“…In the present work for constructing a strong solution to problem (1) − (3) on the whole time interval [0, ∞) we employ the Galerkin approximations method (domain Ω can be unbounded). By this method the solution to a parabolic equation was constructed in work [5] on the bounded time interval [0, ] for each > 0 and in work [6] on an unbounded time interval.…”