# Transversality of stable and Nehari manifolds for a semilinear heat equation

## Related Articles

- On Asymptotic Properties of Solutions of Diffusion Equations. Bagirov, L. A.; Kondratiev, V. A. // Journal of Mathematical Sciences;Apr2003, Vol. 114 Issue 4, p1407
In this work the authors study the conditions for the existence of diffusion equations $\backslash partial\_t\; u(x,t)\; =\; 3DA(x,\backslash partial\; x)\; u(x,t)\; +\; f(u),\; \backslash quad\; A(x,\backslash partial\; x)\; \backslash equiv\; \backslash sum\_\{i,j=3D1\}^n\; \backslash partial\_\{x\_j\}(a\_\{ij\}(x)\backslash partial\_\{x\_i\}),$ in the cylinder Q = 3DÎ© Ã— $\backslash mathbb...$

- Generically Transitive Actions on Multiple Flag Varieties. Devyatov, Rostislav // IMRN: International Mathematics Research Notices;May2014, Vol. 2014 Issue 11, p2972
Let G be a semisimple algebraic group whose decomposition into the product of simple components does not contain simple groups of type A, and PâŠ†G be a parabolic subgroup. Extending the results of Popov [8], we enumerate all triples (G,P,n) such that (a) there exists an open G-orbit on the...

- Solution blowup for the heat equation with double nonlinearity. Korpusov, M. // Theoretical & Mathematical Physics;Sep2012, Vol. 172 Issue 3, p1173
We consider a model initial boundary value problem for the heat equation with double nonlinearity. We use a modified Levin method to prove the solution blowup.

- Global Existence/nonexistence of Sign-Changing Solutions to ut = Î”u + |u|p in Rd. Pinsky, Ross G. // Bulletin of the London Mathematical Society;Jun2005, Vol. 37 Issue 3, p417
Consider the parabolic equationut=Î”u+| u |p in RdÃ—(0,T),u(x,0)=Î¦(x)inRd,up to a maximal time T = Tâˆž, where p > 1. Let p* = 1 + 2/d. It is a classical result that if p â‰¤ p*, then there exist no non-negative, global solutions to the above equation for any choice of Î¦...

- On the Resolution of the Heat Equation with Discontinuous Coefficients. Labbas, Rabah; Moussaoui, Mohand // Semigroup Forum;2000, Vol. 60 Issue 2, p187
We give in this work some results about the existence and uniqueness with optimal regularity for solutions of a parabolic equation in nondivergence form in L[sup q] (0,T;L[sup p] (Omega)) where 1 < p,q < infinity in two cases. We use Lamberton's results (cf. [9]) in the first case and...

- Characterization of the internal stabilizability of the diffusion equation. // Nonlinear Studies;2001, Vol. 8 Issue 2, p193
Analyzes the internal stabilizability of the diffusion equation. Formulation of the problem; Condition for the nonnegative controllability of the diffusion system; Results for a semilinear model of the gas diffusion.

- FIFTH-ORDER NUMERICAL METHODS FOR HEAT EQUATION SUBJECT TO A BOUNDARY INTEGRAL SPECIFICATION. REHMAN, M. A.; TAJ, M. S. A.; BUTT, M. M. // Acta Mathematica Universitatis Comenianae;2010, Vol. 79 Issue 1, p89
In this paper a fifth-order numerical scheme is developed and implemented for the solution of the homogeneous heat equation ut = Î±uxx with a nonlocal boundary condition as well as for the inhomogeneous heat equation ut = uxx+s(x; t) with a nonlocal boundary condition. The results obtained...

- An a priori estimate for the solution of a mixed problem for the heat equation. Kapustin, N. // Differential Equations;Oct2006, Vol. 42 Issue 10, p1447
The article focuses on the analysis of a spectral problem with a spectral parameter in a boundary condition that emerges when considering the action of the heat flow from a medium in which the heat propagation velocity is assumed to be finite. It covered some mathematical expressions of a mixed...

- Solutions for multidimensional fractional anomalous diffusion equations. Long-Jin Lv; Jian-Bin Xiao; Fu-Yao Ren; Lei Gao // Journal of Mathematical Physics;Jul2008, Vol. 49 Issue 7, p073302
In this paper, we investigate the solutions of a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time-dependent diffusion coefficient and N-dimensional case into account, which subjects to natural boundaries and the general initial...