Publicação
Modelling with PDEs
| Resumo: | Taking in consideration the audience, we explore a prospective point of view. We intend to comment on some qualitative aspects and issues concerning the mathematical work of modelization with Partial Differential Equations (PDEs). A class of evolution PDEs: \pa_t u+div f(u)=\eps div b(u,\grad u)+\del div \pa_(\xi) c(u,\grad u), which include generalized Korteweg-de Vries-Burgers equation (when \xi is a space variable) and Benjamin-Bona-Mahony-Burgers equation (when \xi is the time variable), or that of \pa_t u+div f(u)=\del div c(u,\grad u), which can present unexpected dissipative properties. As "\eps,\del-parameters tend to zero we can have failure (i.e., no limit solution at all for \del > O(\eps^\gamma)) or reliability (with different limits: classical-entropy weak-solutions inside an integrity region \del < O(\eps^\gamma) and nonclassicalentropy weak-solutions along \del = O(\eps^\gamma)), according to the \gamma-balance of \eps,\del-strengths and to the ratio between the growths of the b-dissipation and c-dispersion. |
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| Autores principais: | Correia, Joaquim M.C. |
| Assunto: | Modelling Partial Differential Equations Korteweg-de Vries-Burgers equation Benjamin-Bona-Mahony-Burgers equation failure reliability integrity classical-entropy weak-solutions nonclassicalentropy weak-solutions dissipation dispersion |
| Ano: | 2015 |
| País: | Portugal |
| Tipo de documento: | palestra |
| Tipo de acesso: | acesso restrito |
| Instituição associada: | Universidade de Évora |
| Idioma: | inglês |
| Origem: | Repositório Científico da Universidade de Évora |
| Resumo: | Taking in consideration the audience, we explore a prospective point of view. We intend to comment on some qualitative aspects and issues concerning the mathematical work of modelization with Partial Differential Equations (PDEs). A class of evolution PDEs: \pa_t u+div f(u)=\eps div b(u,\grad u)+\del div \pa_(\xi) c(u,\grad u), which include generalized Korteweg-de Vries-Burgers equation (when \xi is a space variable) and Benjamin-Bona-Mahony-Burgers equation (when \xi is the time variable), or that of \pa_t u+div f(u)=\del div c(u,\grad u), which can present unexpected dissipative properties. As "\eps,\del-parameters tend to zero we can have failure (i.e., no limit solution at all for \del > O(\eps^\gamma)) or reliability (with different limits: classical-entropy weak-solutions inside an integrity region \del < O(\eps^\gamma) and nonclassicalentropy weak-solutions along \del = O(\eps^\gamma)), according to the \gamma-balance of \eps,\del-strengths and to the ratio between the growths of the b-dissipation and c-dispersion. |
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