Global in time existence of Sobolev solutions to semi-linear damped sigma-evolution equations in L^q scales

The main goal of this thesis is to prove the global (in time) existence of small data Sobolev solutions to semi-linear damped σ-evolution equations from suitable function spaces basing on L^q spaces by mixing additional L^m regularity for the data on the basis of L^q-L^q estimates for solutions, with q∈(1,∞) and m∈[1,q), to the corresponding linear models. To establish desired results, we would like to apply the theory of modified Bessel functions, Faà di Bruno's formula and Mikhlin-Hörmander multiplier theorem in the treatment of linear problems. In addition, some of modern tools from Harmonic Analysis play a fundamental role to investigate results for the global existence of small data Sobolev solutions to semi-linear problems. Finally, the application of a modified test function method is to devote to the proof of blow-up results for semi-linear damped σ-evolution models, where σ≥1 and δ∈[0,σ) are assumed to be any fractional numbers.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

TU Bergakademie

Year

2020

Author dc:creator

• Dao, Tuan Anh

Contributors dc:contributor

• Reissig, Michael
• Ebert, Marcelo
• Picard, Rainer

• sigma-evolution equations
• damping terms
• L^1 estimates
• global existence
• blow-up