Work

Instantaneous blow-up solutions for nonlinear Sobolev-type equations on the Heisenberg groups

Year: 2024

Type: article

Abstract: 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} $.

Source: Discrete and Continuous Dynamical Systems - S

DOI: 10.3934/dcdss.2024175

Authors: Meiirkhan B. Borikhanov, Michael Ruzhansky, Berikbol T. Torebek

Institutions: Ghent University, Institute of Mathematics and Mathematical Modeling

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond