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Volume 3, Issue 4
On a Class of Quasilinear Parabolic Equations of Second Order with Double-degeneracy

Yin Jingxue

J. Part. Diff. Eq.,3(1990),pp.49-64

Published online: 1990-03

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  • Abstract
In this paper we study the first boundary value problem for nonlinear diffusion equation \frac{∂u}{∂t} + \frac{∂}{∂x}f(u) = \frac{∂}{∂x}A(\frac{∂}{∂x}B(u)) whereA(s) = ∫¹_0a(σ)dσ, B(s) = ∫¹_0b(σ)dσ with a(s) ≥ 0, b(s) ≥ 0. We prove the existence of BV solutions under the much general structural conditions lim_{s → + ∞} A(s) = +∞, lim_{s → - ∞} A(s) = -∞ Moreover, we show the uniqueness without any structural conditions.
  • Keywords

Quasilinear parabolic equation degeneracy existence uniqueness

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COPYRIGHT: © Global Science Press

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@Article{JPDE-3-49, author = {Yin Jingxue}, title = {On a Class of Quasilinear Parabolic Equations of Second Order with Double-degeneracy}, journal = {Journal of Partial Differential Equations}, year = {1990}, volume = {3}, number = {4}, pages = {49--64}, abstract = { In this paper we study the first boundary value problem for nonlinear diffusion equation \frac{∂u}{∂t} + \frac{∂}{∂x}f(u) = \frac{∂}{∂x}A(\frac{∂}{∂x}B(u)) whereA(s) = ∫¹_0a(σ)dσ, B(s) = ∫¹_0b(σ)dσ with a(s) ≥ 0, b(s) ≥ 0. We prove the existence of BV solutions under the much general structural conditions lim_{s → + ∞} A(s) = +∞, lim_{s → - ∞} A(s) = -∞ Moreover, we show the uniqueness without any structural conditions.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5813.html} }
TY - JOUR T1 - On a Class of Quasilinear Parabolic Equations of Second Order with Double-degeneracy AU - Yin Jingxue JO - Journal of Partial Differential Equations VL - 4 SP - 49 EP - 64 PY - 1990 DA - 1990/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5813.html KW - Quasilinear parabolic equation KW - degeneracy KW - existence KW - uniqueness AB - In this paper we study the first boundary value problem for nonlinear diffusion equation \frac{∂u}{∂t} + \frac{∂}{∂x}f(u) = \frac{∂}{∂x}A(\frac{∂}{∂x}B(u)) whereA(s) = ∫¹_0a(σ)dσ, B(s) = ∫¹_0b(σ)dσ with a(s) ≥ 0, b(s) ≥ 0. We prove the existence of BV solutions under the much general structural conditions lim_{s → + ∞} A(s) = +∞, lim_{s → - ∞} A(s) = -∞ Moreover, we show the uniqueness without any structural conditions.
Yin Jingxue. (1990). On a Class of Quasilinear Parabolic Equations of Second Order with Double-degeneracy. Journal of Partial Differential Equations. 3 (4). 49-64. doi:
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