Universal Journal of Mathematics and Mathematical Sciences
Volume 2, Issue 1, Pages 47 - 65
(July 2012)
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THE NUMERICAL SOLUTION OF THE SYSTEM OF THE SECOND-ORDER PARTIAL DIFFERENTIAL EQUATIONS VIA VARIATIONAL APPROACH
Haichun Li
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Abstract: By defining new HL spaces, we develop Riesz representation theorem and Lax-Milgram theorem in new space. We obtain some new results for the systems of the partial differential equations with natural boundary value problem. These results can breakthrough restriction of the application of variational approach to other multi-infection systems. Finally, we give one examples for solving the system of the second-order partial differential equations with constant-coefficients. |
Keywords and phrases: variational approach, boundary value problem, system of the partial differential equation, Sobolev space, extend Riesz representation theorem, extend Lax-Milgram theorem. |
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