Mathematics · Partial Differential Equations
मान लीजिए u(x,t) निम्नलिखित प्रारंभिक-सीमा मान समस्या (initial-boundary value problem) का समाधान है: ∂u∂t = ∂2u∂x2, u(0,t) = u(1,t) = 0, u(x,0) = 2x(1 - x). तो, निम्नलिखित में से कौन सा कथन सत्य है?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1u(x,t) समय t के सापेक्ष तेजी से (exponentially) बढ़ता है
- 2∫01 (u(x,t))2 dx, t का एक घटता हुआ फलन (decreasing function) नहीं है
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सही उत्तर देखें
सभी t ≥ 0 और x &invisitimes; [0,1] के लिए u(x,t) = u(1 - x, t) है
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