Weak self-adjointness and conservation laws for a porous medium equation |
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| Authors: | ML Gandarias |
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| Institution: | 1. Dept. of Earth and Environmental Sciences, Ludwig–Maximilians-Universität München, Theresienstraße 41, D-80333 München, Germany;2. Dept. of Computer Science 10, FAU Erlangen–Nürnberg, Cauerstraße 6, D-91058 Erlangen, Germany;3. Erlangen Regional Computing Centre (RRZE), FAU Erlangen–Nürnberg, Martensstraße 1, D-91058 Erlangen, Germany;4. Institute for Numerical Mathematics (M2), Technische Universität München, Boltzmannstrasse 3, D-85748 Garching b. München, Germany;5. Leibniz Supercomputing Centre (LRZ), Boltzmannstraße 1, 85748 Garching b. München, Germany;1. Universitá di Firenze, Italy;2. National Cheng Kung University, Taiwan;3. National Taiwan University, Taiwan;1. State Key Laboratory of Industrial Control Technology, Department of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China;2. Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai 200240, China;1. School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China;2. Department of Mechanical Engineering, University of Alberta, 4-9 Mechanical Engineering Building, Edmonton, Alberta, Canada T6G 2G8 |
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| Abstract: | The concepts of self-adjoint and quasi self-adjoint equations were introduced by Ibragimov (2006, 2007) 4], 7]. In Ibragimov (2007) 6] a general theorem on conservation laws was proved. In Gandarias (2011) 3] we generalized the concept of self-adjoint and quasi self-adjoint equations by introducing the definition of weak self-adjoint equations. In this paper we find the subclasses of weak self-adjoint porous medium equations. By using the property of weak self-adjointness we construct some conservation laws associated with symmetries of the differential equation. |
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