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PRINCIPAL CURVATURE ESTIMATES FOR THE CONVEX LEVEL SETS OF SEMILINEAR ELLIPTIC EQUATIONS
PRINCIPAL CURVATURE ESTIMATES THE CONVEX LEVEL SETS SEMILINEAR ELLIPTIC EQUATIONS
2014/4/3
We give a positive lower bound for the principal curvature of the strict convex level sets of harmonic functions in terms of the principal curvature of the domain boundary and the norm of the boundary...
A semilinear hyperbolic system violating the null condition
semilinear hyperbolic system null condition Analysis of PDEs
2012/6/7
We consider a two-component system of semilinear wave equations in three space dimensions with quadratic nonlinear terms not satisfying the null condition. We prove small data global existence of the ...
On Control Of Sobolev Norms For Some Semilinear Wave Equations With Localized Data
Control Sobolev Norms Some Semilinear Wave Equations Localized Data
2012/4/16
We establish new bounds of the Sobolev norms of solutions of semilinear wave equations for data lying in the Hs, s<1, closure of compactly supported data inside a ball of radius R, with R a fixed and ...
Almgren-type monotonicity methods for the classification of behavior at corners of solutions to semilinear elliptic equations
Almgren monotonicity formula semilinear elliptic equations conical boundary points
2011/9/19
Abstract: A monotonicity approach to the study of the asymptotic behavior near corners of solutions to semilinear elliptic equations in domains with a conical boundary point is discussed. The presence...
The blow-up theorem of a discrete semilinear wave equation
The blow-up theorem semilinear wave equation Analysis of PDEs
2011/9/1
Abstract: In this paper, the discretization of a nonlinear wave equation whose nonlinear term is a power function is introduced. The difference equation derived by discretizing the nonlinear wave equa...
Boundary value problem for a classical semilinear parabolic equation
positive solution global existence blow-up omega-limit
2011/2/28
In this paper, we study the boundary value problem of the classical semilinear parabolic equations ut − u = |u|p−1u.
Cesari-type Conditions for Semilinear Elliptic Equations with Leading Term Containing Controls
optimal control existence conditions elliptic equations homogenization
2011/1/18
An optimal control problem governed by semilinear elliptic partial differential equations is con-sidered. The equation is in divergence form with the leading term containing controls. By studying the ...
Lower bound of the lifespan of solutions to semilinear wave equations in an exterior domain
Lower bound lifespan of solutions semilinear wave equations
2010/11/30
We consider the Cauchy-Dirichlet problem for semilinear wave equations in a three space dimensional domain exterior to a bounded and non-trapping obstacle. We obtain a detailed estimate for the lower ...
Multiplicity and regularity of large periodic solutions with rational frequency for a class of semilinear wave equations
Multiplicity regularity of large periodic solutions rational frequency semilinear wave equations
2010/12/6
grande, pour une classe d’´equations semilin´eaires avec des conditions p´eriodiques sur le bord: utt − uxx = f(x, u),u(0, t) = u(, t) , ux(0, t) = ux(, t).Notre m´etho...
Capacitary estimates of solutions of semilinear parabolic equations
Heat equation singularities Borel measures Bessel capacities Wiener type test
2010/12/13
We prove that any positive solution of ∂tu − u + uq = 0 (q > 1) in RN × (0,∞) with
initial trace (F, 0), where F is a closed subset of RN can be represented, up to two universal
multipl...
Threshold results for semilinear parabolic systems
Initial boundary value problem Semi-linear parabolic systems
2010/12/9
In this paper, we study initial boundary value problem of semi-linear parabolic systems ut − u = vp (x, t) ∈ × (0, T ).