Results 21 to 30 of about 1,062 (82)
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
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
core +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
wiley +1 more source
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 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
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
doaj +1 more source
Convergence to steady states for radially symmetric solutions to a quasilinear degenerate diffusive Hamilton-Jacobi equation [PDF]
, 2009 Convergence to a single steady state is shown for non-negative and radially symmetric solutions to a diffusive Hamilton-Jacobi equation with homogeneous Dirichlet boundary conditions, the diffusion being the $p$-Laplacian operator, $p\ge 2$, and the ...
Barles, Guy +2 more
core +4 more sources
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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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
core +4 more sources
Well-posedness for a class of nonlinear degenerate parabolic equations
, 2015 In this paper we obtain well-posedness for a class of semilinear weakly degenerate reaction-diffusion systems with Robin boundary conditions. This result is obtained through a Gagliardo-Nirenberg interpolation inequality and some embedding results for ...
A. Bensoussan +10 more
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