Results 21 to 30 of about 1,119 (105)
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
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
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
Refined asymptotics for the infinite heat equation with homogeneous Dirichlet boundary conditions [PDF]
, 2010 The nonnegative viscosity solutions to the infinite heat equation with homogeneous Dirichlet boundary conditions are shown to converge as time increases to infinity to a uniquely determined limit after a suitable time rescaling.
Barles G. +9 more
core +4 more sources
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
Finite mass self-similar blowing-up solutions of a chemotaxis system with non-linear diffusion [PDF]
, 2009 For a specific choice of the diffusion, the parabolic-elliptic Patlak-Keller-Segel system with non-linear diffusion (also referred to as the quasi-linear Smoluchowski-Poisson equation) exhibits an interesting threshold phenomenon: there is a critical ...
A. Blanchet +26 more
core +7 more sources
Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations [PDF]
, 2008 In this article, we provide existence results for a general class of nonlocal and nonlinear second-order parabolic equations. The main motivation comes from front propagation theory in the cases when the normal velocity depends on the moving front in a ...
Alvarez +20 more
core +5 more sources
A cross-diffusion system derived from a Fokker-Planck equation with partial averaging [PDF]
, 2016 A cross-diffusion system for two compoments with a Laplacian structure is analyzed on the multi-dimensional torus. This system, which was recently suggested by P.-L.
Jüngel, Ansgar, Zamponi, Nicola
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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