Pesquisa
Estudo Equações Diferenciais Parciais, com destaque para:
Equações de Reação e Difusão;
Problemas degenerados;
Existência ou não de soluções estáveis;
Comportamento assintótico de soluções.
Controlabilidade
The Mathematics Genealogy Project
Dissertação de Mestrado - UFSCar
Tese de Doutorado - UFSCar
Publicações:
SÔNEGO, M.; BIESDORF, J. - Stable transition layer for the Allen-Cahn equation when the spatial inhomogeneity vanishes on a non-smooth hypersurface in R^n. Mathematical Methods in the Applied Sciences, Volume 46, Issue17, 18096-18110, 2023.[link]
SÔNEGO, M.; ROYCHOWDHURY, R. - A note on control of one-dimensional heterogeneous reaction-diffusion equations. Evolution Equations and Control Theory, Volume 12 (2): 415-422, 2023. [link]
SÔNEGO, M; NASCIMENTO, A. S. - Stable transition layer induced by degeneracy of the spatial inhomogeneities in the Allen-Cahn problem. Discrete & Continuous Dynamical Systems - B, 27(6): 3297-331, 2022. [link]
SÔNEGO, M. - A note on interface formation in singularly perturbed elliptic problems. Complex Variables and Elliptic Equations, v. 67, p. 338-345, 2022. [link]
SÔNEGO, M. - On the internal transition layer to some inhomogeneous semilinear problems: interface location. Journal of Mathematical Analysis and Applications, Volume 502, Issue 2, 125266, 2021. [link]
SÔNEGO, M. - Stable transition layers in an unbalanced bistable equation. Discrete & Continuous Dynamical Systems - B, 26(10): 5627-5640, 2021. [link]
HURTADO, E. J. ; SÔNEGO, M. - On the energy functionals derived from a non-homogeneous p-Laplacian equation: \Gamma - convergence, local minimizers and stable transition layers. Journal of Mathematical Analysis and Applications, v. 483, p. 123634, 2020. [link]
SÔNEGO, M. - On the weakly degenerate Allen-Cahn equation. Advances in Nonlinear Analysis, 9(1), p. 361-371, 2020. [link]
SÔNEGO, M. - Stable solution induced by domain geometry in the heat equation with nonlinear boundary conditions on surfaces of revolution. Discrete & Continuous Dynamical Systems - B, v. 24 (11), p. 5981-5988, 2019. [link]
SÔNEGO, M. - A note on existence of patterns on surfaces of revolution with nonlinear flux on the boundary, Electronic Journal of Qualitative Theory of Differential Equations No. 49, 1-8, 2019. [link]
SÔNEGO, M. - Stability results for a reaction-diffusion problem with mixed boundary conditions and applications to some symmetric cases. Journal of Mathematical Analysis and Applications (Print), v. 466, p. 1190-1210, 2018. [link]
SÔNEGO, M. - Existence of radially symmetric patterns for a diffusion problem with variable diffusivity. Electronic Journal of Qualitative Theory of Differential Equations, v. 2017, p. 1-10, 2017. [link]
SÔNEGO, M. - Patterns in a balanced bistable equation with heterogeneous environments on surfaces of revolution. Differential Equations & Applications, v. 8, p. 521-533, 2016. [link]
SÔNEGO, M. - Stability and instability of solutions of semilinear problems with Dirichlet boundary condition on surfaces of revolution. Electronic Journal of Qualitative Theory of Differential Equations, v. 2016, p. 1-12, 2016. [link]
do NASCIMENTO, A. S. ; SÔNEGO, M. - Stable equilibria to a singularly perturbed reaction-diffusion equation in a degenerated heterogeneous environment. Journal of Mathematical Analysis and Applications (Print), v. 433, p. 1743-1756, 2016. [link]
do NASCIMENTO, A. S. ; SÔNEGO, M. - Stable equilibria of a singularly perturbed reaction-diffusion equation when the roots of the degenerate equation contact or intersect along a non-smooth hypersurface. Journal of Evolution Equations (Printed Ed.), v. 16, p. 317-339, 2016. [link]
do NASCIMENTO, A. S. ; SÔNEGO, M. - Stable Transition Layers to Singularly Perturbed Spatially Inhomogeneous Allen-Cahn Equation. Advanced Nonlinear Studies, v. 15, p. 363-376, 2015. [link]
do NASCIMENTO, A. S. ; SÔNEGO, M. - Patterns on surfaces of revolution in a diffusion problem with variable diffusibility. Electronic Journal of Differential Equations, v. 2014, p. 1-13, 2014. [link]
do NASCIMENTO, A. S. ; SÔNEGO, M. - The roles of diffusivity and curvature in patterns on surfaces of revolution. Journal of Mathematical Analysis and Applications (Print), v. 412, p. 1084-1096, 2014. [link]
do NASCIMENTO, A. S. ; CREMA, J. ; SÔNEGO, M. - Sufficient conditions on diffusivity for the existence and nonexistence of stable equilibria with nonlinear flux on the boundary. Electronic Journal of Differential Equations, v. 2012, p. 1-14, 2012. [link]