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1.
Uniqueness of solutions to a viscous diffusion equation   总被引:1,自引:0,他引:1  
We prove the uniqueness of solutions to the initial boundary value problem of a viscous diffusion equation by means of a regularizing technique based on elliptic operators.  相似文献
2.
This paper deals with the exterior problem of the Newtonian filtration equation with nonlinear boundary sources. The large time behavior of solutions including the critical Fujita exponent are determined or estimated. An interesting phenomenon is illustrated that there exists a threshold value for the coefficient of the lower order term, which depends on the spacial dimension. Exactly speaking, the critical global exponent is strictly less than the critical Fujita exponent when the coefficient is under this threshold, while these two exponents are identically equal when the coefficient is over this threshold. Supported by the NNSF of China and the China Postdoctoral Science Foundation.  相似文献
3.
The paper concerns the well-posedness problem of an evolutionary weighted p-Laplacian with boundary degeneracy. Different from the classical theory for linear equations, it is shown that the degenerate portion of the boundary should be decomposed into two parts: the strongly degenerate boundary on which the equation exhibits hyperbolic characteristics and the weakly degenerate boundary on which the equation still exhibits parabolic characteristics. We formulate reasonably the boundary value condition and establish the existence and uniqueness theorems.  相似文献
4.
This paper deals with a class of linear equations with boundary degeneracy. According to the degenerate ratio, the equations are divided into weakly degenerate ones and strongly degenerate ones, which should be supplemented by different Dirichlet boundary value conditions. After establishing some necessary existence, nonexistence and comparison principles, we investigate the optimal Hölder continuity of weak solutions in these two cases utilizing the Harnack inequality and the Morrey theorem, respectively.  相似文献
5.
This paper is concerned with the existence of positive solutions for the boundary value problem of one-dimensional p-Laplacian with delay. The proof is based on the Guo–Krasnoselskii fixed-point theorem in cones.  相似文献
6.
In this paper, we consider the reaction diffusion equations with spatio-temporal delay, which models the microbial growth in a flow reactor. Nonlocal spatial term, a weighted average in space, arises when the individuals have not necessarily been at the same point in space at previous time. By employing linear chain technique, geometric singular perturbation, and the center manifold theorem, we prove that the steady travelling wave does not only persist, but also it looks qualitatively the same as it do with no delay at all, under the introduction of delays, at least for small delay.  相似文献
7.
This paper is concerned with a class of quasilinear parabolic equations with singularity and arbitrary degeneracy. The existence and uniqueness of generalized solutions to a kind of boundary value problem is established.  相似文献
8.
This paper is concerned with a class of degenerate diffusion equations subject to mixed boundary conditions. Under some structure conditions, we discuss the blow-up property of local solutions and estimate the bounds of “blow-up time.”  相似文献
9.
This paper is devoted to Young measure solutions of a class of forward-backward diffusion equations. Inspired by the idea from a recent work of Demoulini, we first discuss the regular case by introducing the Young measure solutions and prove the existence for such solutions, and then approximate the extreme case by the approach of regularization and establish the existence of Young measure solutions in the class of functions with bounded variation.  相似文献
10.
1.IntroductionInthispaper,weareconcernedwiththebehaviorofsolutionsofthefollowingproblemwheretheinitialdata"o(x)satisfiesnoEW"oo(a,b)and"o(x)20a.e.in(a,6).(1.4)Definition1.AnonnegativefunctionuELoo([0,co);W'loo(n))withfi=(a,b)iscalledaweaksolutionoftheproblem(1.1)--(1.3)ifthefollowingconditionsarefulfilled:(i)acEL'(flx[0,F])foranyT>0,(n)usatisfiestheX..d.yvaluecondition(l.2)intheusualsense.(iii)FOranytestfunctiongbEC2)1(fix[0, co))withgb(a,t)~op(b,t)~0,thereholdstheintegralequalityRecellt…  相似文献
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