The support barrier functions for nonlinear parabolic problems
https://doi.org/10.22405/2226-8383-2024-25-2-235-242
Abstract
Within the framework of the nonlinear method of angular boundary functions, the existence of solutions to nonlinear boundary value problems is proven through the construction of barrier functions. Barrier functions are constructed through specially designated support barriers. The support barriers themselves can also act as barrier functions. The resulting inequalities, in turn, are of independent functional interest.
About the Authors
Alexey Igorevich Denisov
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
postgraduate student
Igor Vasil’evich Denisov
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
References
1. Vasilyeva, A. B., Butuzov, V. F. 1990. “Asymptotic methods in the theory of singular perturbations”, M.: Higher school.
2. Denisov A.I., Denisov I.V., 2024. "Nonlinear method of angular boundary functions for
3. singularly perturbed parabolic problems with cubic nonlinearities” , Chebyshevskii Sbornik,
4. Vol. 25, № . 1, pp. 25–40.
5. Amann H., 1971. “On the Existence of Positive Solutions of Nonlinear Elliptic Boundary Value
6. Problems”, Indiana Univ. Math. J., Vol.21, № 2. pp. 125–146.
7. Sattinger D.H., 1972. “Monotone Methods in Nonlinear Elliptic and Parabolic Boundary Value
8. Problems”, Indiana Univ. Math. J., Vol.21. № 11. pp. 979–1000.
9. Amann H., 1978. “Nonlinear Analysis: coll. of papers in honor of E.H. Rothe / Ed. by L. Cesari
10. et al.”, New York etc: Acad press, cop. – XIII. pp. 1–29.
11. Denisov I.V., 1991. “On the asymptotic expansion of the solution of a singularly perturbed
12. elliptic equation in a rectangle”, Asymptotic methods of the theory of singularly perturbed
13. equations and ill-posed problems: Collection of articles. scientific. tr. - Bishkek: Ilim, p. 37.
14. Denisov I.V., 1995. “Quasilinear Singularly Perturbed Elliptic Equations in a Rectangle”,
15. Computational Mathematics and Mathematical Physics, Vol. 35. № 11. pp. 1341-1350.
Review
For citations:
Denisov A.I., Denisov I.V. The support barrier functions for nonlinear parabolic problems. Chebyshevskii Sbornik. 2024;25(2):235-242. (In Russ.) https://doi.org/10.22405/2226-8383-2024-25-2-235-242
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