On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum
In this paper, we study the nonlinear equation of the form where is the ultra-hyperbolic operator iterated k-times, defined by p + q = n is the dimension of the Euclidean space n, (x, t) = (x1, x2,..., xn, t) n× (0,), k is a positive integer and c is a positive constant. On the suitable conditions f...
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th-cmuir.6653943832-492392018-08-16T02:12:58Z On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum Amnuay Kananthai Kamsing Nonlaopon Mathematics In this paper, we study the nonlinear equation of the form where is the ultra-hyperbolic operator iterated k-times, defined by p + q = n is the dimension of the Euclidean space n, (x, t) = (x1, x2,..., xn, t) n× (0,), k is a positive integer and c is a positive constant. On the suitable conditions for f, u and for the spectrum of the heat kernel, we can find the unique solution in the compact subset of n × (0,). Moreover, if we put k = 1 and q = 0 we obtain the solution of nonlinear equation related to the heat equation. Mathematical subject classification: 35L30, 46F12, 32W30. © 2009 Sociedade Brasileira de Matemática Aplicada e Computacional. 2018-08-16T02:12:58Z 2018-08-16T02:12:58Z 2009-10-21 Journal 18070302 01018205 2-s2.0-70350035723 10.1590/S1807-03022009000200002 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=70350035723&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/49239 |
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Mathematics |
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Mathematics Amnuay Kananthai Kamsing Nonlaopon On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum |
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In this paper, we study the nonlinear equation of the form where is the ultra-hyperbolic operator iterated k-times, defined by p + q = n is the dimension of the Euclidean space n, (x, t) = (x1, x2,..., xn, t) n× (0,), k is a positive integer and c is a positive constant. On the suitable conditions for f, u and for the spectrum of the heat kernel, we can find the unique solution in the compact subset of n × (0,). Moreover, if we put k = 1 and q = 0 we obtain the solution of nonlinear equation related to the heat equation. Mathematical subject classification: 35L30, 46F12, 32W30. © 2009 Sociedade Brasileira de Matemática Aplicada e Computacional. |
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Journal |
| author |
Amnuay Kananthai Kamsing Nonlaopon |
| author_facet |
Amnuay Kananthai Kamsing Nonlaopon |
| author_sort |
Amnuay Kananthai |
| title |
On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum |
| title_short |
On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum |
| title_full |
On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum |
| title_fullStr |
On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum |
| title_full_unstemmed |
On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum |
| title_sort |
on the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum |
| publishDate |
2018 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=70350035723&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/49239 |
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