ISSN:0010-3640    

DOI:10.1002/cpa.3160370502

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1984

数据来源: WILEY

摘要:

AbstractWe prove that under certain conditions the inversion problem for the generalized Radon transform reduces to solving a Fredholm integral equation and we obtain the asymptotic expansion of the symbol of the integral operator in this equation.We consider applications of the generalized Radon transform to partial differential equations with variable coefficients and provide a solution to the inversion problem for the attenuated and exponential Radon transforms.

ISSN:0010-3640    

DOI:10.1002/cpa.3160370503

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1984

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160370504

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1984

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160370505

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1984

数据来源: WILEY

摘要:

AbstractSome laws in physics describe the change of a flux and are represented by parabolic equations of the form (*)\documentclass{article}\pagestyle{empty}\begin{document}$$\frac{{\partial u}}{{\partial t}}=\frac{\partial}{{\partial x_j }}(\eta \frac{{\partial u}}{{ax_j}}-vju),$$\end{document}j≤m, where η andvjare functions of both space and time. We show under quite general assumptions that the solutions of equation (*) with homogeneous Dirichlet boundary conditions and initial conditionu(x, 0) =uo(x)satisfy\documentclass{article}\pagestyle{empty}\begin{document}$$||u||_{p\,}\le c(p)e^{ - dt}||u_o||_p$$\end{document}The decay rated>0 only depends on bounds for η, v andG§ Rmthe spatial domain, while the constantcdepends additionally on which norm is considered. For the solutions of equation (*) with homogeneous Neumann boundary conditions and initial conditionu0(x) ≥ 0 we derive boundsd1u1≤ u(x, t) ≤ d2u2,Wheredi, i= 1, 2, depend on bounds for η, v andG, and theuiare bounds on the initial

ISSN:0010-3640    

DOI:10.1002/cpa.3160370506

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1984

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160370507

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1984

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160370501

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1984

数据来源: WILEY