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Volume 5, Issue 1
The Diffraction Problem and Verigin Problem of Quasilinear Parabolic Equation in Divergence Form for the One-dimensional Case

Lin Zhigui

J. Part. Diff. Eq.,5(1992),pp.35-42

Published online: 1992-05

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  • Abstract
In this paper, we consider the flow of two immiscible fluids in a onedimensional porous medium (the Verigin problem) and obtain a quasilinear parabolic equation in divergence form with the discontinuous coefficients. We prove first the existence and uniqueness of locally classical solution of the diffraction problem and then prove the existence of local solution of the Verigin problem.
  • Keywords

Porous medium discontinuous coefficient diffraction

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COPYRIGHT: © Global Science Press

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@Article{JPDE-5-35, author = {Lin Zhigui}, title = {The Diffraction Problem and Verigin Problem of Quasilinear Parabolic Equation in Divergence Form for the One-dimensional Case}, journal = {Journal of Partial Differential Equations}, year = {1992}, volume = {5}, number = {1}, pages = {35--42}, abstract = { In this paper, we consider the flow of two immiscible fluids in a onedimensional porous medium (the Verigin problem) and obtain a quasilinear parabolic equation in divergence form with the discontinuous coefficients. We prove first the existence and uniqueness of locally classical solution of the diffraction problem and then prove the existence of local solution of the Verigin problem.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5727.html} }
TY - JOUR T1 - The Diffraction Problem and Verigin Problem of Quasilinear Parabolic Equation in Divergence Form for the One-dimensional Case AU - Lin Zhigui JO - Journal of Partial Differential Equations VL - 1 SP - 35 EP - 42 PY - 1992 DA - 1992/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5727.html KW - Porous medium KW - discontinuous coefficient KW - diffraction AB - In this paper, we consider the flow of two immiscible fluids in a onedimensional porous medium (the Verigin problem) and obtain a quasilinear parabolic equation in divergence form with the discontinuous coefficients. We prove first the existence and uniqueness of locally classical solution of the diffraction problem and then prove the existence of local solution of the Verigin problem.
Lin Zhigui. (1970). The Diffraction Problem and Verigin Problem of Quasilinear Parabolic Equation in Divergence Form for the One-dimensional Case. Journal of Partial Differential Equations. 5 (1). 35-42. doi:
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