共查询到20条相似文献,搜索用时 15 毫秒
1.
A. I. Aristov 《Differential Equations》2012,48(6):787-795
We consider an initial-boundary value problem for a nonlinear equation of Sobolev type with variable coefficient multiplying
the power-law nonlinearity. We obtain sufficient conditions for both time-global and time-local solvability. In the case of
local (but not global) solvability, we find two-sided estimates for the lifespan of the solution in the form of quadrature
formulas and indicate special cases in which a closed form of these estimates is possible. 相似文献
2.
《Mathematische Nachrichten》2018,291(5-6):729-758
We are interested in the following question: when regularity properties of a linear differential operator imply solvability of its transpose in the sense of Gevrey ultradistributions? This question is studied for a class of abstract operators that contains the usual differential operators with real‐analytic coefficients. We obtain a new proof of a global result on compact manifolds (global Gevrey hypoellipticity implying global solvability of the transpose), as well as some results in the non‐compact case by means of the so‐called property of non‐confinement of singularities. We provide applications to Hörmander operators, to operators of constant strength and to locally integrable systems of vector fields. We also analyze a conjecture stated in a recent paper of Malaspina and Nicola, which asserts that, in differential complexes naturally arising from locally integrable structures, local solvability in the sense of ultradistributions implies local solvability in the sense of distributions. We establish the validity of the conjecture when the cotangent structure bundle is spanned by the differential of a single first integral. 相似文献
3.
The initial boundary-value problem for the nonlinear nonlocal Sobolev equation is studied. Sufficient conditions for local and for global (with respect to time) solvability are obtained. For the case of local (not global) solvability, upper and lower bounds for the lifespan of the solution are obtained in the form of explicit and implicit formulas. 相似文献
4.
We consider the unique solvability of the inverse problem of determining the right-hand side of a parabolic equation with the leading coefficient depending on time and space variables under a final overdetermination condition. We obtain two types of conditions that are sufficient for the local solvability of the inverse problem and also prove the so-called Fredholm solvability of the inverse problem under study. 相似文献
5.
Keisuke Uchikoshi 《Mathematische Nachrichten》2005,278(3):318-343
We consider local solvability of semilinear hyperbolic Cauchy problems for Gevrey functions. To obtain a general result, we define the notion of irregularities, and we give a criterion for the local solvability. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
M. O. Korpusov 《Mathematical Notes》2013,93(1-2):90-101
A new model three-dimensional third-order equation of Hamilton-Jacobi type is derived. For this equation, the initial boundary-value problem in a bounded domain with smooth boundary is studied and local solvability in the strong generalized sense is proved; in addition, sufficient conditions for the blow-up in finite time and sufficient conditions for global (in time) solvability are obtained. 相似文献
7.
A. V. Chernov 《Russian Mathematics (Iz VUZ)》2012,56(3):55-65
We study a nonlinear controlled functional operator equation in an ideal Banach space. We establish sufficient conditions
for the global solvability for all controls from a given set, and obtain a pointwise estimate for solutions. Using upper and
lower estimates of the functional component in the right-hand side of the initial equation (with a fixed operator component),
we obtain majorant and minorant equations. We prove the stated theorem, assuming the monotonicity of the operator component
in the right-hand side and the global solvability of both majorant andminorant equations. We give examples of the reduction
of controlled initial boundary value problems to the equation under consideration. 相似文献
8.
Maxim O. Korpusov Dmitry V. Lukyanenko Alexander A. Panin 《Mathematical Methods in the Applied Sciences》2020,43(17):9829-9873
We establish the local (in time) solvability in the classical sense for the Cauchy problem and first and second boundary-value problems on the half-line for a nonlinear equation similar to Benjamin-Bona-Mahony-Bürgers-type equation. We also derive an a priori estimate that implies sufficient blow-up conditions for the second boundary-value problem. We obtain analytically an upper bound of the blow-up time and refine it numerically using Richardson effective accuracy order technique. 相似文献
9.
This work is devoted to the solvability and finite time blow-up of solutions of the Cauchy problem for the dissipative Boussinesq equation in all space dimension. We prove the existence and uniqueness of local mild solutions in the phase space by means of the contraction mapping principle. By establishing the time-space estimates of the corresponding Green operators, we obtain the continuation principle. Under some restriction on the initial data, we further study the results on existence and uniqueness of global solutions and finite time blow-up of solutions with the initial energy at three different level. Moreover, the sufficient and necessary conditions of finite time blow-up of solutions are given. 相似文献
10.
A. I. Aristov 《Computational Mathematics and Mathematical Physics》2012,52(10):1417-1427
The initial boundary value problem for a nonlinear nonhomogeneous equation of Sobolev type used for modeling nonstationary processes in semiconductors is examined. It is proved that this problem is uniquely solvable at least locally in time. Sufficient conditions for the problem to be solvable globally in time are found, as well as sufficient conditions for the local (but not global) solvability. In the case of only local solvability, upper and lower estimates for the time when a solution exists are determined in the form of either explicit or quadrature formulas. 相似文献
11.
Natalia P. Bondarenko 《Mathematical Methods in the Applied Sciences》2020,43(11):7009-7021
The paper deals with the Sturm–Liouville eigenvalue problem with the Dirichlet boundary condition at one end of the interval and with the boundary condition containing entire functions of the spectral parameter at the other end. We study the inverse problem, which consists in recovering the potential from a part of the spectrum. This inverse problem generalizes partial inverse problems on finite intervals and on graphs and also the inverse transmission eigenvalue problem. We obtain sufficient conditions for global solvability of the studied inverse problem, which prove its local solvability and stability. In addition, application of our main results to the partial inverse Sturm–Liouville problem on the star-shaped graph is provided. 相似文献
12.
This paper is concerned with the well-posedness and asymptotic behavior of Dirichlet initial boundary value problem for a singular parabolic p-biharmonic equation with logarithmic nonlinearity. We establish the local solvability by the technique of cut-off combining with the methods of Faedo–Galerkin approximation and multiplier. Meantime, by virtue of the family of potential wells, we use the technique of modified differential inequality and improved logarithmic Sobolev inequality to obtain the global solvability, infinite and finite time blow-up phenomena, and derive the upper bound of blow-up time as well as the estimate of blow-up rate. Furthermore, the results of blow-up with arbitrary initial energy and extinction phenomena are presented. 相似文献
13.
V. L. Kamynin 《Mathematical Notes》2005,77(3-4):482-493
We study the unique solvability of the inverse problem of determining the righthand side of a parabolic equation whose leading coefficient depends on both the time and the spatial variable under an integral overdetermination condition with respect to time. We obtain two types of condition sufficient for the local solvability of the inverse problem as well as study the so-called Fredholm solvability of the inverse problem under consideration.Translated from Matematicheskie Zametki, vol. 77, no. 4, 2005, pp. 522–534.Original Russian Text Copyright © 2005 by V. L. Kamynin.This revised version was published online in April 2005 with a corrected issue number. 相似文献
14.
Conditions for existence of a global strong solution to one class of nonlinear evolution equations in Hilbert space 总被引:1,自引:1,他引:0
We obtain a criterion of global strong solvability for one class of nonlinear evolution equations in Hilbert space. 相似文献
15.
We consider one-dimensional equations of the type of the Yajima–Oikawa–Satsuma ion acoustic wave equation and prove the local solvability. Using the test function method, we obtain sufficient conditions for solution blow-up and estimate the blow-up time. 相似文献
16.
We analyze the local solvability of a control system with mixed constraints and control constraints. We obtain a sufficient
condition for the local solvability of the control system under the assumption of smoothness and 2-regularity of the mapping
g specifying the mixed constraints. For the case in which the mapping g is not smooth, a sufficient condition for the local solvability is obtained under the assumption of coverability of g. 相似文献
17.
We obtain a criterion of global strong solvability for one class of nonlinear evolution equations in Hilbert space. 相似文献
18.
Numerical Algorithms - Inthis paper, we study the global uniqueness and solvability of tensor complementarity problems for $\mathcal {H}_{+}$-tensors. We obtain a sufficient condition of the global... 相似文献
19.
Solvability of Cauchy's problem in for fractional Hamilton–Jacobi equation (1.1) with subcritical nonlinearity is studied here both in the classical Sobolev spaces and in the locally uniform spaces. The first part of the paper is devoted to the global in time solvability of subcritical equation (1.1) in locally uniform phase space, a generalization of the standard Sobolev spaces. Subcritical growth of the nonlinear term with respect to the gradient is considered. We prove next the global in time solvability in classical Sobolev spaces, in Hilbert case. Regularization effect is used there to guarantee global in time extendibility of the local solution. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
20.
E. V. Radkevich 《Journal of Mathematical Sciences》2012,181(5):701-750
We continue the study of the global solvability of the Cauchy problem for discrete kinetic equations and consider the general
case of complex data of the problem. We prove the existence of a global solution and obtain its representation. Bibliography:
10 titles. 相似文献