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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| Main Authors: | , |
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| Format: | Journal |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=70350035723&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/59733 |
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| Institution: | Chiang Mai University |
| Summary: | 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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