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Page 2232 of Mathematical Reviews Vol. , Issue 84f [page]

1984 Mathematical Reviews  
The theme of the conference was on time- dependent nonlinear partial differential equations; in particular, the majority of the speakers lectured either on shock waves or reaction-diffusion equations and  ...  of singularities for nonlinear hyperbolic partial differential equations (pp. 45-56); Ronald J.  ... 

List of talks

1985 Journal of Computational and Applied Mathematics  
(Taiwan): Symbolic solution for partial differential equation by associative approach. CUYT A. (Belgium): A review of multivariate Pad6 approximation. DARGAHI-NOUBARY G.R.  ...  (Belgium): The auxiliary boundary element method for time dependent problems. DE SITTER J.  ...  (West Germany): Numerical treatment of time dependent coupled partial differential equations based on error minimization. ERLICH M. (France): On stochastic models of sedimentation process.  ... 
doi:10.1016/0377-0427(85)90003-2 fatcat:fzodha5wmzainl37dzusulyoje

Page 3273 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews  
-bounded solution for some interval of time, and that this solution is unique. Condi- tions for Hélder continuity of the solution to the linear equation were also given.  ...  of the solutions of such equations to that of a nonlinear stochastic partial differential equation which describes the evolution law of the curvature of F.  ... 

Page 3051 of Mathematical Reviews Vol. , Issue 94f [page]

1994 Mathematical Reviews  
Popiotek, On the Cauchy-Dirichlet problem for an equation of third order (473- 483); J. Priiss, Linear evolutionary integral equations on the line (485-513); I. A. Shishmarév and P. I.  ...  theory of systems of linear partial differential equations (275- 283); Albrecht Holderrieth, Commuting multiplicative perturba- tions (285-290); Sen Zhong Huang and F.  ... 

Page 797 of Mathematical Reviews Vol. , Issue 94b [page]

1994 Mathematical Reviews  
(RS-AOS-C; Moscow) On the limit behavior of a bounded solution of a system of first- order evolution quasilinear partial differential equations under an unbounded time increase. (Russian.  ...  Differential Integral Equations 6 (1993), no. 3, 613-626. The author considers the large-time behavior of the solution of the problem u, = (u"-!  ... 

Page 1488 of Mathematical Reviews Vol. , Issue 95c [page]

1995 Mathematical Reviews  
In this interesting paper the authors extend the well-known Flo- quet theory for time-periodic linear ordinary differential equations to scalar parabolic partial differential equations (1) u,; = ux. +  ...  In the linear case it is proven that given any solution to the hyper- bolic equations there is always a solution to the diffusion equation which after a short time stays very close to it for all times.  ... 

Page 5417 of Mathematical Reviews Vol. , Issue 91J [page]

1991 Mathematical Reviews  
(E-MADC-AM) Boundedness and blow up for a semilinear reaction-diffusion system. J. Differential Equations 89 (1991), no. 1, 176-202.  ...  (F-PARIS9-A) Interior gradient bounds for the mean curvature equation by viscosity solutions methods. Differential Integral Equations 4 (1991), no. 2, 263-275.  ... 

A waveform relaxation algorithm with overlapping splitting for reaction diffusion equations

Martin J. Gander
1999 Numerical Linear Algebra with Applications  
It is shown for a scalar reaction diffusion equation with variable diffusion coefficient that the new waveform relaxation algorithm converges superlinearly for bounded time intervals and linearly for unbounded  ...  Two classical convergence results state linear convergence on unbounded time intervals for linear systems of ODEs under some dissipation assumption and superlinear convergence on bounded time intervals  ...  of the iteration on bounded time intervals.  ... 
doi:10.1002/(sici)1099-1506(199903)6:2<125::aid-nla152>3.0.co;2-4 fatcat:inpngfkj5vfobftejj4nf5eteq

Page 5187 of Mathematical Reviews Vol. , Issue 98H [page]

1998 Mathematical Reviews  
Similarly, in this paper, we define the integral solution for a stochastic evolution equation with a state-dependent diffusion term and prove that there exists a unique integral solution of the stochastic  ...  Stochastic Equations 4 (1996), no. 3, 251-272. Summary: “We study a linear differential equation in R" with almost constant coefficients that depend linearly on a Markov diffusion process.  ... 

Book Review: Global classical solutions for nonlinear evolution equations

Walter A. Strauss
1993 Bulletin of the American Mathematical Society  
Evolution equations are partial differential equations whose solutions one studies as functions of a distinguished independent variable t, called time.  ...  Specifically, one asks for ( 1 ) local existence (to find classes of functions for which at least one solution exists for at least a nontrivial interval of time), (2) global existence (to find classes  ...  Nevertheless, it would make a nice choice for a part of a graduate course designed as a sequel to a course on linear partial differential equations.  ... 
doi:10.1090/s0273-0979-1993-00415-4 fatcat:l6brapwlnzcbtbfhjjcoqfjjbq

Partial differential systems with non-local nonlinearities: generation and solutions

Margaret Beck, Anastasia Doikou, Simon J. A. Malham, Ioannis Stylianidis
2018 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
We develop a method for generating solutions to large classes of evolutionary partial differential systems with nonlocal nonlinearities.  ...  For arbitrary initial data, the solutions are generated from the corresponding linearized equations. The key is a Fredholm integral equation relating the linearized flow to an auxiliary linear flow.  ...  The work of M.B. was partially supported by US National Science Foundation grant DMS-1411460.  ... 
doi:10.1098/rsta.2017.0195 pmid:29507179 fatcat:q6vtbp7bmja4lk5hbdhzejt7vm

Page 5432 of Mathematical Reviews Vol. , Issue 85m [page]

1985 Mathematical Reviews  
A. 85m:35003 A modification of the accelerated analytic method for approximate integration of linear partial differential equations. (Russian)  ...  Dey, An implicit numerical solver for nonlinear hy- perbolic partial differential equations (pp. 79-91); William Layton, On the behavior over long time intervals of finite difference and finite element  ... 

Page 4236 of Mathematical Reviews Vol. , Issue 97G [page]

1997 Mathematical Reviews  
The book is fairly well written and provides a good introduction to this interesting field of nonlinear partial differential equations.  ...  Summary: “The asymptotic stability of shock profiles is proved for a nonconvex convection-diffusion equation by using weighted energy estimates for the integrated equation.  ... 

Page 4631 of Mathematical Reviews Vol. , Issue 95h [page]

1995 Mathematical Reviews  
The unitary symmetries of linear partial differential equations are employed to decompose some Hilbert spaces of solutions preserved by the symmetries into direct integrals in the sense of Mackey.  ...  Then H decomposes as a direct integral H = {, H; di, where H, are solutions of cer- tain ordinary differential operators depending on A. J.  ... 

Page 2347 of Mathematical Reviews Vol. , Issue 95d [page]

1995 Mathematical Reviews  
Schultz (1-WIM; Milwaukee, WI) 65M _ Partial differential equations, initial value and time-dependent initial-boundary value problems 954:65075 95d:65072 65M06 35A35 Jédar, L.  ...  That is, they consider a system of nonlinear equations with nonlinear diffusion and thermal capacity coefficients.  ... 
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