Results 21 to 30 of about 1,099 (88)
Critical global asymptotics in higher‐order semilinear parabolic equations
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 60, Page 3809-3825, 2003., 2003 We consider a higher‐order semilinear parabolic equation ut = −(−Δ)mu − g(x, u) in ℝN × ℝ+, m > 1. The nonlinear term is homogeneous: g(x, su) ≡ |s|p−1sg(x, u) and g(sx, u) ≡ |s|Qg(x, u) for any s ∈ ℝ, with exponents P > 1, and Q > −2m. We also assume that g satisfies necessary coercivity and monotonicity conditions for global existence of solutions ...
Victor A. Galaktionov
wiley +1 more source
Anisotropic nonlinear diffusion with absorption: existence and extinction
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 3, Page 427-434, 1996., 1994 The authors prove that the nonlinear parabolic partial differential equation with homogeneous Dirichlet boundary conditions and a nonnegative initial condition has a nonnegative generalized solution u. They also give necessary and sufficient conditions on the constitutive functions φij and f which ensure the existence of a time t0 > 0 for which u ...
Alan V. Lair, Mark E. Oxley
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Global strong solutions to the planar compressible magnetohydrodynamic equations with large initial data and vaccum [PDF]
, 2016 This paper considers the initial boundary problem to the planar compressible magnetohydrodynamic equations with large initial data and vacuum. The global existence and uniqueness of large strong solutions are established when the heat conductivity ...
Fan, Jishan, Huang, Shuxiang, Li, Fucai
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Null controllability for a degenerate population model in divergence form via Carleman estimates
Advances in Nonlinear Analysis, 2019 In this paper we consider a degenerate population equation in divergence form depending on time, on age and on space and we prove a related null controllability result via Carleman estimates.
Fragnelli Genni
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A system of impulsive degenerate nonlinear parabolic functional‐differential inequalities
International Journal of Stochastic Analysis, Volume 8, Issue 1, Page 59-68, 1995., 1994 A theorem about a system of strong impulsive degenerate nonlinear parabolic functional‐differential inequalities in an arbitrary parabolic set is proved. As a consequence of the theorem, some theorems about impulsive degenerate nonlinear parabolic differential inequalities and the uniqueness of a classical solution of an impulsive degenerate nonlinear ...
Ludwik Byszewski
wiley +1 more source
On distributional solutions of local and nonlocal problems of porous medium type [PDF]
, 2017 We present a theory of well-posedness and a priori estimates for bounded distributional (or very weak) solutions of $$\partial_tu-\mathfrak{L}^{\sigma,\mu}[\varphi(u)]=g(x,t)\quad\quad\text{in}\quad\quad \mathbb{R}^N\times(0,T),$$ where $\varphi$ is ...
del Teso, Félix +2 more
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On the parabolic potentials in degenerate‐type heat equation
International Journal of Stochastic Analysis, Volume 4, Issue 2, Page 147-160, 1991., 1991 Using distributions theory technique we introduce parabolic potentials for the heat equation with one time‐dependent coefficient (not everywhere positive and continuous) at the highest space‐derivative, discuss their properties, and apply obtained results to three illustrative problems.
Igor Malyshev
wiley +1 more source
Rate of Convergence to Barenblatt Profiles for the Fast Diffusion Equation [PDF]
, 2011 We study the asymptotic behaviour of positive solutions of the Cauchy problem for the fast diffusion equation near the extinction time. We find a continuum of rates of convergence to a self-similar profile.
A. Blanchet +19 more
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A conditional regularity result for p-harmonic flows [PDF]
, 2015 We prove an $\varepsilon$-regularity result for a wide class of parabolic systems $$ u_t-\text{div}\big(|\nabla u|^{p-2}\nabla u) = B(u, \nabla u) $$ with the right hand side $B$ growing like $|\nabla u|^p$.
Katarzyna Ewa Mazowiecka +4 more
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The nonlinear diffusion equation of the ideal barotropic gas through a porous medium
Open Mathematics, 2017 The nonlinear diffusion equation of the ideal barotropic gas through a porous medium is considered. If the diffusion coefficient is degenerate on the boundary, then the solutions may be controlled by the initial value completely, the well-posedness of ...
Zhan Huashui
doaj +1 more source