arXiv subjects

Carlos Alberto Reyes Peña

Publications and source records attributed to Carlos Alberto Reyes Peña.

2 recordsLinked to original sources

arXiv2024

Existence of weak solutions for a degenerate Goursat type linear problem

For a generalization of the Gellerstedt operator with mixed-type Dirichlet boundary conditions to a suitable Tricomi domain, we prove the existence and uniqueness of weak solutions of the linear problem and for a generalization of this problem. The classical method introduced by Didenko, which study the energy integral argument, will be used to prove estimates for a specific Tricomi domain.

math.AP↗

arXiv2024

Nonexistence results for a degenerate Goursat type Problem

For a generalization of the Gellerstedt operator with Dirichlet boundary conditions in a Tricomi domain. We establish Pohožaev-type identities and prove the nonexistence of nontrivial regular solutions. Furthermore, we investigate the critical exponent phenomenon for power-type nonlinearities, characterized by the critical exponent of a weighted Sobolev embedding.

math.AP↗