Stability of fast parallel MHD shock waves in polytropic gas |
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| Affiliation: | 1. College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, Zhejiang, China;2. Czech Technical University, Faculty of Civil Engineering, Dept. of Math., Thakurova 7, 166 29 Prague, Czech Republic;3. Institute of Hydrodynamics, Academy of Sciences of the Czech Republic, Pod Paťankou 30/5, 166 12 Prague 6, Czech Republic;1. Division of Cancer Epidemiology, German Cancer Research Center, Heidelberg, Germany;2. Division of Epigenomics and Cancer Risk Factors, German Cancer Research Center, Heidelberg, Germany;3. Department of Oncology, Oncology Centre, Cambridge University Hospital NHS Foundation Trust, United Kingdom (UK);4. Institute of Cancer Research and Royal Marsden NHS Foundation Trust, London, UK;6. Department of Genetics, University of Leicester, Leicester, UK;5. Advanced Radiation Biology Research Program, National Institute of Radiological Sciences, Chiba, Japan;7. Radiation Medicine Program, Princess Margaret Cancer Centre, University Health Network, Toronto, Ontario, Canada;11. Centre for Cancer Genetic Epidemiology, University of Cambridge, Strangeways Research Laboratory, Cambridge, UK;12. Department of Oncology, Oncology Centre, Cambridge University Hospital NHS Foundation Trust, University of Cambridge, Cambridge, UK;8. The Institute of Cancer Research, Clinical Trials and Statistics Unit, Sutton, UK;10. Department of Cancer Studies and Molecular Medicine, University of Leicester, Leicester, UK;9. Department of Radiation Oncology, Icahn School of Medicine at Mount Sinai, New York, NH;71. Department of Radiation Oncology, Staedtisches Klinikum Karlsruhe, Karlsruhe, Germany;112. Clinic for Radiation Therapy and Radiation Oncology, St. Vincentius-Kliniken gAG, Karlsruhe, Germany;123. Department of Radiation Oncology, University of Heidelberg, Heidelberg, Germany;84. Clinic for Radiotherapy and Radiation Oncology, Klinikum Ludwigshafen, Ludwigshafen am Rhein, Germany;106. Department of Radiation Oncology, University Medical Centre Mannheim, University of Heidelberg, Mannheim, Germany;95. Institute of Cancer Sciences, The University of Manchester, Manchester Academic Health Science Centre, Manchester, UK;1. Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;2. School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, PR China;1. Ludwig Boltzmann Institute for Experimental and Clinical Traumatology – Austrian Cluster for Tissue Regeneration, AUVA Research Center, Vienna, Austria;2. AUVA Trauma Center Meidling, Vienna, Austria;3. Kuros Biosurgery AG, Zurich, Switzerland;4. Baxter Innovations GmbH, Vienna, Austria |
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| Abstract: | The stability of plane shock waves in Magnetohydrodynamics for an ideal medium is studied. Stability results are obtained for the special case of fast parallel shock waves in a polytropic gas. Linear stability is proved for a polytropic gas with arbitrary γ. The domain of structural (nonlinear) stability, where the uniform Lopatinsky condition is fulfilled for the stability problem, is found. |
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