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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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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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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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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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Conditional symmetry of a porous medium equation
Physica D: Nonlinear Phenomena, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhdanov, R. Z., Lahno, V. I.
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A Porous Medium Equation with Variable Nonlinearity
2015We devote this chapter to study the homogeneous Dirichlet problem for the semilinear parabolic equation which generalizes the Porous Medium Equation.
Stanislav Antontsev, Sergey Shmarev
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The porous medium equation with measure data
Journal of Evolution Equations, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Porous Medium Equation with Critical Strong Absorption
2004In this chapter we continue the study of critical phenomena in the model of diffusion-absorption introduced in the previous chapter. We concentrate here on the influence of a stronger absorption term which creates a singularity of the type called finite-time extinction. In the rescaled sense this leads to a singularly perturbed dynamical system.
Victor A. Galaktionov +1 more
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