Self-similar blow-up in parabolic equations of Monge--Ampère type [PDF]
arXiv, 2009 We propose nonlinear parabolic equations of Monge--Amp\'ere (M--A) type that admit regional, single poin, and global blow-up of similarity type. A similar model is derived for a fourth-order M--A flow.
arxiv
Very Singular Similarity Solutions and Hermitian Spectral Theory for Semilinear Odd-Order PDEs [PDF]
arXiv, 2009 Very singular self-similar solutions of semilinear odd-order PDEs are studied on the basis of a Hermitian-type spectral theory for linear rescaled odd-order operators.
arxiv
On source-type solutions and the Cauchy problem for a doubly degenerate sixth-order thin film equation I. Local oscillatory properties [PDF]
arXiv, 2009 Local oscillatory and other properties of source-type solutions of doubly nonlinear sixth-order parabolic thin film equations are studied.
arxiv
On Continuous Branches of Very Singular Similarity Solutions of the Stable Thin Film Equation [PDF]
arXiv, 2010 Continuous branches of similarity solutions of the fourth-order stable thin film equation are studied.
arxiv
Continuity of the temperature in a multi-phase transition problem. [PDF]
Math Ann, 2022 Gianazza U, Liao N.
europepmc +1 more source
Feynman-Kac theorems for generalized diffusions [PDF]
arXiv, 2012 We find Feynman-Kac type representation theorems for generalized diffusions. To do this we need to establish existence, uniqueness and regularity results for equations with measure-valued coefficients.
arxiv
Harnack's inequality for doubly nonlinear equations of slow diffusion type. [PDF]
Calc Var Partial Differ Equ, 2021 Bögelein V +3 more
europepmc +1 more source
On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient
Electronic Journal of Differential Equations, 2002 We study the Cauchy problem for the nonlinear (possibly strongly) degenerate parabolic transport-diffusion equation $$ partial_t u + partial_x (gamma(x)f(u))=partial_x^2 A(u), quad A'(cdot)ge 0, $$ where the coefficient $gamma(x)$ is possibly ...
John D. Towers +2 more
doaj
On the Time Derivative in a Quasilinear Equation [PDF]
Trans. R. Norw. Soc. Sci. Lett. 2008(2), 1-7, 2016 The time derivative (in the sense of distributions) of the solutions to the Evolutionary p-Laplace Equation is proved to be a function in a local Lebesgue space.
arxiv
A degenerate migration-consumption model in domains of arbitrary dimension
Advanced Nonlinear StudiesIn a smoothly bounded convex domain Ω⊂Rn ${\Omega}\subset {\mathbb{R}}^{n}$ with n ≥ 1, a no-flux initial-boundary value problem forut=Δuϕ(v),vt=Δv−uv, $$\begin{cases}_{t}={\Delta}\left(u\phi \left(v\right)\right),\quad \hfill \\ {v}_{t}={\Delta}v-uv ...
Winkler Michael
doaj +1 more source