Instantaneous blow-up solutions for nonlinear Sobolev-type equations on the Heisenberg groups
In this paper, we study two nonlinear Sobolev-type equations on the Heisenberg groups. We show that the problems do not admit nontrivial local weak solutions, i.e. 'instantaneous blow-up' occurs, using the nonlinear capacity method. Namely, by choosing suitable test functions, we will prove an instantaneous blow-up for any initial conditions $ u_0, \, u_1\in L^q(\mathbb{H}^n) $ with $ q\leq \frac{Q}{Q-2} $.
Authors
- Michael Ruzhansky (ORCID: https://orcid.org/0000-0001-8633-5570)
- Berikbol T. Torebek (ORCID: https://orcid.org/0000-0002-2354-2377)
- Meiirkhan B. Borikhanov (ORCID: https://orcid.org/0000-0002-5687-0561)
Institutions
- Ghent University (BE)
- Institute of Mathematics and Mathematical Modeling (KZ)
Publication Details
- Journal
- Discrete and Continuous Dynamical Systems - S
- Published
- 2024-09-26
- DOI
- https://doi.org/10.3934/dcdss.2024175
- Citations
- 1
- Primary Topic
- Advanced Mathematical Physics Problems
- Type
- article
- Field-Weighted Citation Impact
- 0.89
Funders
- Engineering and Physical Sciences Research Council