Blow up solutions for Sinh-Gordon equation with residual mass-Reference-Cited by-同舟云学术

Blow up solutions for Sinh-Gordon equation with residual mass

Published:2022-09-26 Issue:6 Volume:61 Page:
ISSN:0944-2669
Container-title:Calculus of Variations and Partial Differential Equations
language:en
Short-container-title:Calc. Var.

Author:

Ao Weiwei,Jevnikar Aleks^ORCID,Yang Wen

Abstract

AbstractWe are concerned with the Sinh-Gordon equation in bounded domains. We construct blow up solutions with residual mass exhibiting either partial or asymmetric blow up, i.e. where both the positive and negative part of the solution blow up. This is the first result concerning residual mass for the Sinh-Gordon equation showing in particular that the concentration-compactness theory with vanishing residuals of Brezis-Merle can not be extended to this class of problems.

Funder

Università degli Studi di Udine

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Analysis

Link

https://link.springer.com/content/pdf/10.1007/s00526-022-02317-1.pdf

Reference29 articles.

1. Ao, W., Jevnikar, A., Yang, W.: On the boundary behavior for the blow up solutions of the sinh-Gordon equation and rank $$N$$ Toda systems in bounded domains. Int. Math. Res. Not. (IMRN) 2020(23), 9386–9419 (2020)

2. Bartolucci, D., Lin, C.S.: Uniqueness results for mean field equations with singular data. Comm. PDEs 34(7), 676–702 (2009)

3. Battaglia, L., Jevnikar, A., Malchiodi, A., Ruiz, D.: A general existence result for the Toda system on compact surfaces. Adv. Math. 285, 937–979 (2015)

4. Baraket, S., Pacard, F.: Construction of singular limits for a semilinear elliptic equation in dimension $$2$$. Calc. Var. PDEs 6, 1–38 (1998)

5. Brezis, H., Merle, F.: Uniform estimates and blow-up behavior for solutions of $$-\Delta u = V (x)e^u$$ in two dimensions. Comm. PDEs 16, 1223–1253 (1991)