Bartuccelli paper appears in JMAA

Michele Bartuccelli’s paper on “Explicit estimates on the torus for the sup-norm and the dissipative length scale of solutions of the Swift-Hohenberg equation in one and two space dimensions” has been accepted for publication in the Journal of Mathematical Analysis and its Applications.  In the paper, he has obtained explicit and accurate estimates of the sup-norm for solutions of the Swift-Hohenberg Equation (SHE) in one and two space dimensions. By using the best (so far) available estimates of the embedding constants which appear in the classical functional interpolation inequalities used in the study of solutions of dissipative partial differential equations, he has evaluated in an explicit manner the values of the sup-norm of the solutions of the SHE. In addition he has calculated the so-called time-averaged dissipative length scale associated to the above solutions.  The final form electronic version can be found here.