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Displaying 81 – 100 of 285

Existence of solutions for infinite systems of parabolic equations with functional dependence

Anna Pudełko (2005)

Annales Polonici Mathematici

The Cauchy problem for an infinite system of parabolic type equations is studied. General operators of parabolic type of second order with variable coefficients are considered and the system is weakly coupled. We prove the existence and uniqueness of a bounded solution under Carathéodory type conditions and its differentiability, as well as the existence and uniqueness in the class of functions satisfying a natural growth condition. Both results are obtained by the fixed point method.

Existence of solutions with exponential growth for nonlinear differential-functional parabolic equations

Agnieszka Bartłomiejczyk, Henryk Leszczyński (2014)

Annales Polonici Mathematici

We consider the Cauchy problem for nonlinear parabolic equations with functional dependence. We prove Schauder-type existence results for unbounded solutions. We also prove existence of maximal solutions for a wide class of differential functional equations.

Expansion of embedded curves with tuning angle greater than - ... .

B. Chow, Lii-Perng Liou, Dong-Ho Tsai (1996)

Inventiones mathematicae

Explicit difference schemes for nonlinear differential functional parabolic equations with time dependent coefficients-convergence analysis

A. Poliński (2006)

Annales Polonici Mathematici

We study the initial-value problem for parabolic equations with time dependent coefficients and with nonlinear and nonlocal right-hand sides. Nonlocal terms appear in the unknown function and its gradient. We analyze convergence of explicit finite difference schemes by means of discrete fundamental solutions.

Exponential convergence for a periodically driven semilinear heat equation

Nikos Zygouras (2009)

Annales de l'I.H.P. Analyse non linéaire

Exponential stability of solutions of the Cauchy problem for a diffusion equation with absorption with a distribution initial condition.

Orewczyk, Joanna (2002)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Finite difference approximations for a class of nonlocal parabolic equations.

Lin, Yanping, Xu, Shuzhan, Yin, Hong-Ming (1997)

International Journal of Mathematics and Mathematical Sciences

Finite difference discretization with variable mesh of the Schrodinger equation in a variable domain

Georgios D. Akrivis, Vassilios A. Dougalis (1990)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Finite element analyis of exponentially fitted Lumped schemes for time-dependent convection-diffusion problems.

Martin Stynes, Wen Guo (1993/1994)

Numerische Mathematik

Front propagation for nonlinear diffusion equations on the hyperbolic space

Hiroshi Matano, Fabio Punzo, Alberto Tesei (2015)

Journal of the European Mathematical Society

We study the Cauchy problem in the hyperbolic space $ℍ^{n} (n \geq 2)$ for the semilinear heat equation with forcing term, which is either of KPP type or of Allen-Cahn type. Propagation and extinction of solutions, asymptotical speed of propagation and asymptotical symmetry of solutions are addressed. With respect to the corresponding problem in the Euclidean space $ℝ^{n}$ new phenomena arise, which depend on the properties of the diffusion process in $ℍ^{n}$ . We also investigate a family of travelling wave solutions, named...

Fundamental decay mode and asymptotic behaviour of positive semigroups

Ivo Marek (1980)

Czechoslovak Mathematical Journal

Generalized Fokker-Planck equations and convergence to their equilibria

Piotr Biler, Grzegorz Karch (2003)

Banach Center Publications

We consider extensions of the classical Fokker-Planck equation uₜ + ℒu = ∇·(u∇V(x)) on $ℝ^{d}$ with ℒ = -Δ and V(x) = 1/2|x|², where ℒ is a general operator describing the diffusion and V is a suitable potential.

Generic behaviour of one-dimensional blow up patterns

M. A. Herrero, J. J. L. Velázquez (1992)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Global and blowup solutions of quasilinear parabolic equation with critical Sobolev equation and lower energy initial value.

Tan, Zhong, Yao, Zheng-An (2001)

Journal of Inequalities and Applications [electronic only]

Global Attractors for a Class of Semilinear Degenerate Parabolic Equations on $ℝ^{N}$

Cung The Anh, Le Thi Thuy (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

We prove the existence of global attractors for the following semilinear degenerate parabolic equation on $ℝ^{N}$ : ∂u/∂t - div(σ(x)∇ u) + λu + f(x,u) = g(x), under a new condition concerning the variable nonnegative diffusivity σ(·) and for an arbitrary polynomial growth order of the nonlinearity f. To overcome some difficulties caused by the lack of compactness of the embeddings, these results are proved by combining the tail estimates method and the asymptotic a priori estimate method.

Global attractors for problems with monotone operators

Alexandre N. Carvalho, Jan W. Cholewa, Tomasz Dlotko (1999)

Bollettino dell'Unione Matematica Italiana

L'esistenza di attrattori globali per equazioni paraboliche semilineari è stata estensivamente studiata da molti autori mentre il caso quasilineare è stato meno considerato e ancora esistono molti problemi aperti. L'obiettivo di questo lavoro è di studiare, da un punto di vista astratto, l'esistenza di attrattori globali per equazioni paraboliche quasilineari con parte principale monotona. I risultati ottenuti vengono applicati a problemi parabolici degeneri del secondo ordine e di ordine superiore....

Global existence and nonexistence for semiliniear parabolic systems with nonlinear boundary conditions.

Joachim Escher (1989)

Mathematische Annalen

Global existence and regularity of solutions for complex Ginzburg-Landau equations

Stéphane Descombes, Mohand Moussaoui (2000)

Bollettino dell'Unione Matematica Italiana

Si considerano equazioni di Ginzburg-Landau complesse del tipo $u_{t} - α Δ u + P ({|u|}^{2}) u = 0$ in $R^{N}$ dove $P$ è polinomio di grado $K$ a coefficienti complessi e $α$ è un numero complesso con parte reale positiva $ℜ α$ . Nell'ipotesi che la parte reale del coefficiente del termine di grado massimo $P$ sia positiva, si dimostra l'esistenza e la regolarità di una soluzione globale nel caso $|α| < C ℜ α$ , dove $C$ dipende da $K$ e $N$ .

Gradient descent and fast artificial time integration

Uri M. Ascher, Kees van den Doel, Hui Huang, Benar F. Svaiter (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

The integration to steady state of many initial value ODEs and PDEs using the forward Euler method can alternatively be considered as gradient descent for an associated minimization problem. Greedy algorithms such as steepest descent for determining the step size are as slow to reach steady state as is forward Euler integration with the best uniform step size. But other, much faster methods using bolder step size selection exist. Various alternatives are investigated from both theoretical and practical...

Grid adjustment based on a posteriori error estimators

Karel Segeth (1993)

Applications of Mathematics

The adjustment of one-dimensional space grid for a parabolic partial differential equation solved by the finite element method of lines is considered in the paper. In particular, the approach based on a posteriori error indicators and error estimators is studied. A statement on the rate of convergence of the approximation of error by estimator to the error in the case of a system of parabolic equations is presented.

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