LECTURE NOTES ON APPLIED MATHEMATICS
Jun 17, 2009 · 2 Since this equation holds for arbitrary regions , it follows that, for smooth func-tions, (1.2) u t= r ~q+ ˙: Equation (1.2) is the di erential form of conservation of Q. When the source term ˙is nonzero, (1.2) is often called, with more accuracy, a balance law for Q, rather than a conservation law, but we won’t insist on this distinction. 2.
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