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The qualitative properties of solutions of a Neumann problem for the singular parabolic equation ut = (u^m-1 ux)x (-1 〈 m ≤0) is studied in this paper. It is proved that there exists a unique global smooth solution which depends on the initial value. The large time behavior of the solutions is also discussed. 相似文献
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Dagmar Medková 《Integral Equations and Operator Theory》2009,63(2):227-247
The Neumann problem for the Poisson equation is studied on a general open subset G of the Euclidean space. The right-hand side is a distribution F supported on the closure of G. It is shown that a solution is the Newton potential corresponding to a distribution B ∈ε (clG), where ε(clG) is the set of all distributions with finite energy supported on the closure of G. The solution is looked for in this form and the original problem reduces to the integral equation TB = F. If the equation TB = F is solvable, then the solution is constructed by the Neumann series. The necessary and sufficient conditions for the solvability
of the equation TB = F is given for NTA domains with compact boundary.
The research was supported by the Academy of Sciences of the Czech Republic, Institutional Research Plan No. AV0Z10190503. 相似文献
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A. G. Losev 《Differential Equations》2017,53(12):1595-1604
The behavior of solutions of the Poisson equation on noncompact Riemannian manifolds of a special form is studied. Sharp conditions for the unique solvability of the Dirichlet problem on the reconstruction of solutions of the Poisson equation from continuous boundary data at infinity are found. 相似文献
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This paper deals with the local solvability of initial value problem for Kaup-Kupershmidt equations. Indeed, using Bourgain method, we prove that the Cauchy problem of Kaup-Kupershmidt equation is local well-posed in H8 whenever s 〉 9/8, which improves the former results in [5]. 相似文献
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A. V. Tarasenko 《Russian Mathematics (Iz VUZ)》2018,62(3):53-59
We study unique solvability of a nonlocal problem for equations of mixed type in a finite domain. This equation contains the partial fractional Riemann–Liouville derivative. The boundary condition of the problem contains a linear combination of operators of fractional differentiation in the sense of Riemann–Liouville of values of function derivative on the degeneration line and generalized operators of fractional integro-differentiation in the sense of M. Saigo. The uniqueness theorem of the problem is proved by a modified Tricomi method. The existence of solutions is equivalently reduced to the solvability of Fredholm integral equation of the second kind. 相似文献
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《数学的实践与认识》2013,(23)
将Nedelec J C所提出的三棱柱单元构造方式运用到Poisson方程,利用Raviart、Thomas所提出的混合元变分形式,并利用Fortin准则证明了离散BB条件,最后给出了误差估计. 相似文献
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V. A. Litovchenko 《Ukrainian Mathematical Journal》2004,56(2):228-243
We describe spaces of test functions that generalize S-type and W-type spaces. In these spaces, we establish the complete solvability of the Cauchy problem for one equation of integral form with Bessel fractional integro-differential operator. 相似文献
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In terms of coefficients of an equation under consideration, we derive 16 variants of collections of conditions of resolvability of this equation in quadratures. Every collection consists of three identities that interconnect five coefficients appearing in left-hand side of an equation. 相似文献
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Dagmar Medková 《Czechoslovak Mathematical Journal》2003,53(2):377-395
A necessary and sufficient condition for the continuous extendibility of a solution of the Neumann problem for the Laplace equation is given. 相似文献
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The present paper deals with a nonlinear viscoelastic equation having a dissipation term. With the equation some classical and non classical boundary conditions are combined. Based on some a priori bounds, iteration processes and density arguments, we simultaneously solve the nonlinear and the associated linear problems. 相似文献