It is proved that in the case of smooth spatial domain Q the space of initial data (i.e., the space of initial functions for which the strong solution exists) coincides with Sobolev space H1 (Q).
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, the second boundary-value problem for parabolic differentialdifference equation is considered.
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Key Findings & Data:In this paper, the second boundary-value problem for parabolic differentialdifference equation is considered.
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Conclusion & Impact:It is proved that in the case of smooth spatial domain Q the space of initial data (i.e., the space of initial functions for which the strong solution exists) coincides with Sobolev space H1 (Q).
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this paper, the second boundary-value problem for parabolic differentialdifference equation is considered. It is proved that in the case of smooth spatial domain Q the space of initial data (i.e., the space of initial functions for which the strong solution exists) coincides with Sobolev space H1 (Q).
Özet
Bu makalede, parabolik diferensiyel-fark denklemi için ikinci sınır değer problemi ele alındı. Q düzgün uzaysal bölge olması durumunda başlangıç değeri uzayının (yani, güçlü bir çözümü var olan başlangıç fonksiyonlar uzayı) H1 (Q) Sobolev uzayına denk olduğu ispatlandı.
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Cite This Article
SELİTSKİİ, A. M. (2022). Parabolik diferensiyel-fark denklemi için ikinci sınır değer probleminin başlangıç değeri uzayı. Contemporary Analysis and Applied Mathematics, Cilt: 1 - Sayı: 1, 34–41. https://ajindex.com/articles/476495
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