Cauchy problem for a semilinear Éidel’man parabolic equation
We obtain conditions for the existence and uniqueness of a generalized solution of the Cauchy problem for the equation $$u_1 + \sum_{|\alpha|=|\beta|=2}(-1)^{|\alpha|}D^{\alpha}_x(a_{\alpha \beta}(z, t)D_x^{\beta}u) - \sum_{|\alpha|=|\beta|=1}(-1)^{|\alpha|}D^{\alpha}_y(b_{\alpha \beta}(z, t)D_y^{\...
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| Date: | 2008 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2008
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3178 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We obtain conditions for the existence and uniqueness of a generalized solution of the Cauchy problem for the equation
$$u_1 + \sum_{|\alpha|=|\beta|=2}(-1)^{|\alpha|}D^{\alpha}_x(a_{\alpha \beta}(z, t)D_x^{\beta}u) -
\sum_{|\alpha|=|\beta|=1}(-1)^{|\alpha|}D^{\alpha}_y(b_{\alpha \beta}(z, t)D_y^{\beta}u) +$$
$$+ \sum_{|\alpha|=1}c_{\alpha}(z, t) D^{\alpha}_zu + c(z, t, u) =
\sum_{|\alpha|\leq2}(-1)^{|\alpha|}D^{\alpha}_x f_{\alpha}(z, t) -
\sum_{|\alpha|=1}D^{\alpha}_y g_{\alpha}(z, t)$$
in Tikhonov's class. |
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