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On the Stochastic Porous Medium Equation
Journal of Differential Equations, 2006 The author proves existence and uniqueness for the Cauchy problem and the initial-boundary value problem \[ u_{t}=\sum_{i=1}^{n}\partial_{x_{i}}(| u| ^{p-2}\partial_{x_{i}}u)+\sum_{j=1}^{\infty}f_{j}{dB_{j}\over dt},\quad (t,x)\in (0,T)\times G, \] \(u=0\), \((t,x)\in (0,T)\times\partial G\), \(u(0,x)=u_0(x)\), \(x\in G\), where \(G\) is a bounded ...
Jong Uhn Kim
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Porous Medium Equation with Absorption
SIAM Journal on Mathematical Analysis, 1998The paper studies the approach to the steady state for the porous medium equation with absorption in a bounded domain in \(\mathbb{R}^N\) with time-independent Dirichlet conditions. Special attention is given to the case where the solution of the steady state vanishes in a interior region (known as a dead core).
Bandle, Catherine +2 more
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Harnack estimates for a kind of porous medium equation
Applied Mathematics Letters, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Feida Jiang, Xinyi Shen, Hui Wu
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Improved regularity for the inhomogeneous Porous Medium Equation
Journal of Mathematical Analysis and Applications, 2021The author studies the sharp regularity for the solutions of \[u_t-\operatorname{div}(m|u|^{m-1}\nabla u) = f \in L^{q,r},\] with \(m> 1\), in function of the optimal Hölder exponent for solutions of the homogeneous case. This result extends the recent one obtained by Araújo, Maia and Urbano \textit{D. J. Araújo} et al. [J. Anal. Math. 140, No. 2, 395--
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The Cauchy Problem of the Porous Medium Equation with Absorption
Journal of Partial Differential Equations, 1994Summary: We study the existence of solution for the Cauchy problem \(u_ t= \Delta u^ m- u^ p\), \(u(x,0)= u_ 0(x)\), \(x\in\mathbb{R}^ n\). We show how the growth condition of initial trace is determined by the absorption.
Zhao, Junning, Liu, Huizhao
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Linearization of dynamic equations for a saturated porous medium
International Applied Mechanics, 2009The authors present equations of saturated porous medium mechanics which take into account the effect of the deformation tensor of the fluid and the initial state of the medium. A special attention is paid to the linearization and the justification of the basic nonlinear equations of the theory.
Israfilov, R. M., Khotenko, I. N.
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Fundamental Solution of the Anisotropic Porous Medium Equation
Acta Mathematica Sinica, English Series, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Song, Binheng, Jian, Huaiyu
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2006
Abstract The heat equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it come to be fairly well understood.
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Abstract The heat equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it come to be fairly well understood.
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Weak solutions of the porous medium equation in a cylinder
Transactions of the American Mathematical Society, 1993We show that if D ⊂
Dahlberg, Björn E. J., Kenig, Carlos E.
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Doubly Nonlinear Equations of Porous Medium Type
Archive for Rational Mechanics and Analysis, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Verena Bögelein +3 more
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