NOLOKAL BOSHLANG'ICH VA NEYMAN CHEGARAVIY SHARTLI ISSIQLIK TARQALISH TENGLAMASI UCHUN MANBANI ANIQLASHNING TESKARI MASALASI.
Keywords:
Teskari masala, issiqlik tarqalish tenglamasi, nolokal shart, Neyman sharti, manba funksiyasi, Furye usuli, korrektlik.Abstract
Ushbu maqolada issiqlik tarqalish tenglamasi uchun noma’lum manba funksiyasini aniqlashning teskari masalasi tadqiq etiladi. Masalaning o‘ziga xosligi shundaki, unda klassik boshlang‘ich shart o‘rniga nolokal boshlang‘ich shart va chegarada Neyman sharti (issiqlik oqimi) berilgan. Manba funksiyasini topish uchun qo‘shimcha integral ko‘rinishdagi ma’lumotdan foydalanilgan. Masalaning yagonaligi va mavjudligi Furye qatorlari usuli yordamida isbotlangan hamda yechimning berilgan ma’lumotlarga bog‘liqligi tahlil qilingan.
References
1. Tikhonov, A. N., & Arsenin, V. Y. (1977). Solutions of Ill-posed Problems. Winston & Sons. (Teskari masalalar bo'yicha fundamental asar).
2. Kozhanov, A. I. (2014). Composite Type Equations and Inverse Problems. De Gruyter. (Murakkab turdagi tenglamalar va teskari masalalar uchun metodik qo'llanma).
3. Prilepko, A. I., Orlovsky, D. G., & Vasin, I. A. (2000). Methods for Solving Inverse Problems in Mathematical Physics. Marcel Dekker. (Manba funksiyasini topish usullari bayon etilgan).
4. Bitsadze, A. V., & Samarskii, A. A. (1969). "Some elementary boundary-value problems for elliptic equations with non-local conditions". Doklady Akademii Nauk SSSR. (Nolokal shartlarning nazariy asosi).
5. Cannon, J. R. (1984). The One-Dimensional Heat Equation. Cambridge University Press. (Issiqlik tarqalish tenglamasi bo'yicha klassik darslik).
6. Ashyralyev, A., & Sobolevskii, P. E. (2004). New Difference Schemes for Partial Differential Equations. Birkhäuser. (Nolokal shartli masalalarning sonli yechimlari haqida).
7. Isakov, V. (2017). Inverse Problems for Partial Differential Equations. Springer. (Parabolik tenglamalar uchun teskari masalalar tahlili).
8. Samarskii, A. A., & Vabishchevich, P. N. (2007). Numerical Methods for Solving Inverse Problems of Mathematical Physics. Walter de Gruyter. (Metodlar bo'limi uchun foydali manba).
9. Umarov, S. (2015). Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols. Springer. (Zamonaviy nolokal va kasr tartibli masalalar uchun).
10. Zikirov, O. S. (2020). Xususiy hosilali differensial tenglamalar. Universitet. (O'zbek tilidagi fundamental darsliklardan biri).
