Results 21 to 30 of about 221 (39)

On centre subspace behaviour in thin flm equations [PDF]

arXiv, 2009
It is shown that the fourth-order parabolic thin film equation with critical absorption admits the large time behaviour, where special logarithmic perturbations enter the standard source-type asymptotics. Such asymptpotic phenomena on existence of logarithmic factors are known for semilinear heat equation with absorption since the 1980s.
arxiv  

On nonexistence of Baras--Goldstein type for higher-order parabolic equations with singular potentials [PDF]

arXiv, 2009
An analogy of nonexistence result by Baras and Goldstein (1984), for the heat equation with inverse singular potential, is proved for 2mth-order linear parabolic equations with Hardy-supercritical singular potentials. Extensions to other linear and nonlinear singular PDEs are discussed.
arxiv  

Higher integrability for doubly nonlinear parabolic systems. [PDF]

SN Partial Differ Equ Appl, 2022
Bögelein V, Duzaar F, Scheven C.
europepmc   +1 more source

Regional, single point, and global blow-up for the fourth-order porous medium type equation with source [PDF]

arXiv, 2009
Three types of blow-up for a fourth-order degenerate reaction-diffusion equation are studied by a combination of analytic and numerical methods. At the critical values of parameters, there occurs a variational problem with a countable set of solutions obtained by Lysternik--Shnirelman category theory, which then are extended to neighbouring values of ...
arxiv  

On Regularized Systems of Equations for Gas Mixture Dynamics with New Regularizing Velocities and Diffusion Fluxes. [PDF]

Entropy (Basel), 2023
Zlotnik A, Lomonosov T.
europepmc   +1 more source

Incomplete self-similar blow-up in a semilinear fourth-order reaction-diffusion equation [PDF]

arXiv, 2009
It is shown that self-similar blow-up for a fourth-order reaction-diffusion equation is incomplete in the sense that, in general, there exists a self-similar extension of solutions after blow-up. Other types of complete blow-up of non self-similar form are discussed.
arxiv  

Three tupes of self-similar blow-up for the fourth-order p-Laplacian equaiton with source: variational and branching approaches [PDF]

arXiv, 2009
The fourth-order quasilinear reaction-diffusion equation with a p-Laplacian operator is shown to admit three types of blow-up. Self-similar patterns are first constructed for the regional blow-up case, where the rescaled problem admits a variational setting. Next, these were extended via a branching approach to non-variational problems.
arxiv  

Variational Approach to Complicated Similarity Solutions of Higher-Order Nonlinear PDEs. II [PDF]

arXiv, 2011
Some higher-order quasilinear parabolic, hyperbolic, and nonlinear dispersion equations are shown to admit various blow-up, extinction, and travelling wave solutions, which reduce to variational problems admitting countable families of compactly supported solutions.
arxiv  

Sturmian Multiple Zeros for Stokes and Navier--Stokes Equations in $\re^3$ via Solenoidal Hermite Polynomials [PDF]

arXiv, 2011
Multiple spatial zero formations for Stokes and Navier-Stokes equations in three dimensions are shown to occur according to nodal sets of solenoidal Hermite polynomials. Extensions to well-posed Burnett equations with the bi-harmonic viscosity operator are also discussed.
arxiv  

Ricci flows which terminate in cones [PDF]

arXiv
We prove that a complete solution to the Ricci flow on $M\times [-T, 0)$ which has quadratic curvature decay on some end of $M$ and converges locally smoothly to the end of a cone on that neighborhood as $t\nearrow 0$ must be a gradient shrinking soliton.
arxiv