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Peer-reviewedCC BY 4.0Axioms

Wave Equations with Lipschitz Nonlinearity of Combined Power and Logarithmic Type: Existence of Global Solutions

  • Milena Dimova1
  • Natalia Kolkovska1
  • Nikolai Kutev1
  1. 1Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
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Abstract

In this paper, we investigate wave equations with a general class of Lipschitz nonlinearities combining power and logarithmic terms. Local existence and uniqueness of weak solutions are established via the Galerkin method. For nonlinearities of defocusing type, we prove global existence of the weak solutions for arbitrary initial energy. In particular, we provide examples of globally defined solutions with negative initial energy.

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Cite

BibTeXRIS
BibTeX
@article{dimova2026wave,
  title = {{Wave Equations with Lipschitz Nonlinearity of Combined Power and Logarithmic Type: Existence of Global Solutions}},
  author = {Milena Dimova and Natalia Kolkovska and Nikolai Kutev},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15100781},
  url = {https://www.mdpi.com/2075-1680/15/10/781},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Wave Equations with Lipschitz Nonlinearity of Combined Power and Logarithmic Type: Existence of Global Solutions
AU  - Milena Dimova
AU  - Natalia Kolkovska
AU  - Nikolai Kutev
PY  - 2026
DA  - 2026/10/18
JO  - Axioms
DO  - 10.3390/axioms15100781
UR  - https://www.mdpi.com/2075-1680/15/10/781
AB  - In this paper, we investigate wave equations with a general class of Lipschitz nonlinearities combining power and logarithmic terms. Local existence and uniqueness of weak solutions are established via the Galerkin method. For nonlinearities of defocusing type, we prove global existence of the weak solutions for arbitrary initial energy. In particular, we provide examples of globally defined solutions with negative initial energy.
SN  - 2075-1680
ER  -