共查询到20条相似文献,搜索用时 15 毫秒
1.
Mitsuhiro Nakao 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):2236-2248
We prove the global existence of the so-called H2 solutions for a nonlinear wave equation with a nonlinear dissipative term and a derivative type nonlinear perturbation. To show the boundedness of the second order derivatives we need a precise energy decay estimate and for this we employ a ‘loan’ method. 相似文献
2.
We consider the inhomogeneous Neumann initial–boundary value problem for the nonlinear Schrödinger equation, formulated on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial–boundary value problem and the asymptotic behavior of solutions for large time. 相似文献
3.
Erik Wahlén 《NoDEA : Nonlinear Differential Equations and Applications》2007,13(5-6):643-653
We prove a blow-up result for a nonlinear shallow water equation by showing that certain initial profiles evolve into breaking
waves. 相似文献
4.
Semi-hyperbolic patches are the regions in which one family out of two nonlinear families of characteristics starts on sonic curves and ends on transonic shock waves. This type of region appears frequently in the two-dimensional Riemann problem for the Euler equations and its simplified models and a few other situations. We construct a semi-hyperbolic patch of solution to the two-dimensional nonlinear wave system with Chaplygin gas equation of state by approaching the problem as a Goursat-type boundary value problem which has a sonic curve as the degenerate boundary. 相似文献
5.
We study the inverse scattering problem for the nonlinear Schrödinger equation and for the nonlinear Klein–Gordon equation with the generalized Hartree type nonlinearity. We reconstruct the nonlinearity from knowledge of the scattering operator, which improves the known results. 相似文献
6.
N. Mavinga 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(15):5171-5188
We study the existence of (generalized) bounded solutions existing for all times for nonlinear parabolic equations with nonlinear boundary conditions on a domain that is bounded in space and unbounded in time (the entire real line). We give a counterexample which shows that a (weak) maximum principle does not hold in general for linear problems defined on the entire real line in time. We consider a boundedness condition at minus infinity to establish (one-sided) L∞-a priori estimates for solutions to linear boundary value problems and derive a weak maximum principle which is valid on the entire real line in time. We then take up the case of nonlinear problems with (possibly) nonlinear boundary conditions. By using comparison techniques, some (delicate) a priori estimates obtained herein, and nonlinear approximation methods, we prove the existence and, in some instances, positivity and uniqueness of strong full bounded solutions existing for all times. 相似文献
7.
Paschalis Karageorgis 《Journal of Differential Equations》2005,219(2):259-305
We study the nonlinear wave equation with a sign-changing potential in any space dimension. If the potential is small and rapidly decaying, then the existence of small-amplitude solutions is driven by the nonlinear term. If the potential induces growth in the linearized problem, however, solutions that start out small may blow-up in finite time. 相似文献
8.
We study the nonlinear self-adjointness of a general class of quasilinear 2D second order evolution equations which do not possess variational structure. For this purpose, we use the method of Ibragimov, devised and developed recently. This approach enables one to establish the conservation laws for any differential equation. We first obtain conditions determining the self-adjoint sub-class in the general case. Then, we establish the conservation laws for important particular cases: the Ricci Flow equation, the modified Ricci Flow equation and the nonlinear heat equation. 相似文献
9.
Mitsuhiro Nakao 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(7):2158-2169
We derive an energy decay estimate for solutions to the initial-boundary value problem of a semilinear wave equation with a nonlinear localized dissipation. To overcome a difficulty related to derivative-loss mechanism we employ a ‘loan’ method. 相似文献
10.
This paper deals with the blow-up of positive solutions for a nonlinear parabolic equation subject to nonlinear boundary conditions. We obtain the conditions under which the solutions may exist globally or blow up in a finite time, by a new approach. Moreover, upper estimates of the “blow-up time”, blow-up rate and global solutions are obtained also. 相似文献
11.
This paper deals with a nonclassical initial boundary value problem for a two dimensional parabolic equation with Bessel operator. We prove the existence and uniqueness of the weak solution of the given nonlinear problem. We start by solving the associated linear problem. After writing this latter in its operator form, we establish an a priori bound from which we deduce the uniqueness of the strong solution. For the solvability of the associated linear problem, we prove that the range of the operator generated by the considered problem is dense. On the basis of the obtained results of the linear problem, we apply an iterative process to establish the existence and uniqueness of the nonlinear problem. 相似文献
12.
Rémi Carles 《Journal of Functional Analysis》2003,203(2):453-493
We consider a nonlinear semi-classical Schrödinger equation for which it is known that quadratic oscillations lead to focusing at one point, described by a nonlinear scattering operator. If the initial data is an energy bounded sequence, we prove that the nonlinear term has an effect at leading order only if the initial data have quadratic oscillations; the proof relies on a linearizability condition (which can be expressed in terms of Wigner measures). When the initial data is a sum of such quadratic oscillations, we prove that the associate solution is the superposition of the nonlinear evolution of each of them, up to a small remainder term. In an appendix, we transpose those results to the case of the nonlinear Schrödinger equation with harmonic potential. 相似文献
13.
We prove the existence of global decaying solutions to the exterior problem for the Klein–Gordon equation with a nonlinear localized dissipation and a derivative nonlinearity. To derive the required estimates of solutions we employ a ‘loan’ method. 相似文献
14.
Alessio Pomponio 《Journal of Differential Equations》2006,227(1):258-281
Coupled nonlinear Schrödinger systems describe some physical phenomena such as the propagation in birefringent optical fibers, Kerr-like photorefractive media in optics and Bose-Einstein condensates. In this paper, we study the existence of concentrating solutions of a singularly perturbed coupled nonlinear Schrödinger system, in presence of potentials. We show how the location of the concentration points depends strictly on the potentials. 相似文献
15.
Felipe Benitez 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(14):4682-4697
We consider the initial-boundary value problem on a half-line for the KdV equation with Landau damping. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time. 相似文献
16.
We prove the existence of solutions to nonlinear free boundary problem with singularities at given points. 相似文献
17.
Said Mesloub Fatiha Mesloub 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(10):3195-3208
For a coupled nonlinear singular system of thermoelasticity with one space dimension, we consider its initial boundary value problem on an interval. For one of the unknowns a classical condition is replaced by a nonlocal constraint of integral type. Because of the presence of a memory term in one of the equations and the presence of a weighted boundary integral condition, the solution requires a delicate set of techniques. We first solve a particular case of the given nonlinear problem by using a functional analysis approach. On the basis of the results obtained and an iteration method we establish the well-posedness of solutions in weighted Sobolev spaces. 相似文献
18.
João Paulo Dias 《Journal of Differential Equations》2011,251(3):492-503
We consider a system coupling a multidimensional semilinear Schrödinger equation and a multidimensional nonlinear scalar conservation law with viscosity, which is motivated by a model of short wave-long wave interaction introduced by Benney (1977). We prove the global existence and uniqueness of the solution of the Cauchy problem for this system. We also prove the convergence of the whole sequence of solutions when the viscosity ε and the interaction parameter α approach zero so that α=o(ε1/2). We also indicate how to extend these results to more general systems which couple multidimensional semilinear systems of Schrödinger equations with multidimensional nonlinear systems of scalar conservation laws mildly coupled. 相似文献
19.
We investigate quasilinear systems of parabolic partial differential equations with fully nonlinear boundary conditions on
bounded or exterior domains in the setting of Sobolev–Slobodetskii spaces. We establish local wellposedness and study the
time and space regularity of the solutions. Our main results concern the asymptotic behavior of the solutions in the vicinity
of a hyperbolic equilibrium. In particular, the local stable and unstable manifolds are constructed.
Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday 相似文献
20.
Andrés I. Ávila Jianfu Yang 《NoDEA : Nonlinear Differential Equations and Applications》2006,12(4):459-479
We proved a multiplicity result for a nonlinear elliptic system in RN. The functional related to the system is strongly indefinite. We investigated the relation between the number of solutions
and the topology of the set of the global maxima of the coefficients. 相似文献