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Supersonic flow of a Chaplygin gas past a delta wing

Science China Mathematics 2022年第11期65卷 2271-2296页

作者： Bingsong Long Chao Yi School of Mathematics and Statistics Huanggang Normal UniversityHuanggang 438000China Center for Mathematical Sciences Huazhong University of Science and TechnologyWuhan 430074China

We consider the problem of supersonic flow of a Chaplygin gas past a delta wing with a shock or a rarefaction wave attached to the leading *** flow under study is described by the three-dimensional steady Euler *** conical coordinates,this problem can be reformulated as a boundary value problem for a nonlinear equation of mixed *** type of this equation depends fully on the solutions of the problem itself,and thus it cannot be determined in *** overcome the difficulty by establishing a crucial Lipschitz estimate,and finally prove the unique existence of the solution via the method of continuity.

关键词： supersonic flow delta wing Chaplygin gas boundary value problem equation of mixed type

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The Existence and Uniqueness of a New Boundary Value Problem(type of Problem“E”)for a Class of Semi Linear(Power type Nonlinearities)mixed Hyperbolic-Elliptic System equations of Keldysh type with Changing Time Direction

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Acta Mathematicae Applicatae Sinica 2022年第4期38卷 763-777页

作者： Mahammad A.NURMAMMADOV Shemakhi Astrophysical Observatory named after Nasreddin Tusi of the Azerbaijan's Ministry of Science and EducationAZ-5626ShemakhadistrictPirkuliAzerbaijan

In present work studied the new boundary value problem for semi linear(Power-type nonlinearities)system equations of mixed hyperbolic-elliptic Keldysh type in the multivariate dimension with the changing time *** problem and equation belongs to the modern level partial differential *** methods of functional analysis,topological methods,“ε”-*** continuation by the parameter at the same time with aid of a prior estimates,under assumptions conditions on coefficients of equations of system,the existence and uniqueness of generalized and regular solutions of a boundary problem are established in a weighted Sobolev's *** this work one of main idea consists of show that the new boundary value problem which investigated in case of linear system equations can be well-posed when added nonlinear terms to this linear system equations,moreover in this case constructed new weithged spaces,the identity between of strong and weak solutions is established.

关键词： changing time direction weighted Sobolev space equation of mixed type strong weak and regular solution eqution of Keldysh type

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