Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6417332 | Journal of Mathematical Analysis and Applications | 2016 | 20 Pages |
Abstract
We prove the existence of global in time weak nonnegative solutions to a family of nonlinear fourth-order evolution equations, parametrized by a real parameter qâ(0,1], which includes the well known thin-film (q=1/2) and the Derrida-Lebowitz-Speer-Spohn (DLSS) equation (q=1), subject to periodic boundary conditions in one spatial dimension. In contrast to the gradient flow approach in [25], our method relies on dissipation property of the corresponding entropy functionals (Tsallis entropies) resulting in required a priori estimates, and extends the existence result from [25] to a wider range of the family members, namely to 0
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Mario Bukal,