Results 21 to 30 of about 1,145 (69)
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
Large time behavior of solutions for the porous medium equation with a nonlinear gradient source
Boundary Value Problems, 2014 This paper deals with the large time behavior of non-negative solutions for the porous medium equation with a nonlinear gradient source ut=Δum+|∇ul|q, (x,t)∈Ω×(0,∞), where l≥m>1 and 1 ...
Nan Li +3 more
semanticscholar +2 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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THE EVOLUTION OF AN ANISOTROPIC HYPERBOLIC SCHRODINGER MAP HEAT FLOW
, 2015 Solution of Schrödinger map heat flow equation with applied field in 2-dimensional H2 space is obtained. Two different methods are used to construct the norm −1 exact solution. The solution admit a finite time singularity or a global smooth property. AMS
P. Zhong
semanticscholar +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
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
core +1 more source