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Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 03/2016, Volume 2016, Issue 712, pp. 51 - 80
We study a quasilinear parabolic equation of forward-backward type, under assumptions on the nonlinearity which hold for a wide class of mathematical models,... 
MATHEMATICS | PSEUDOPARABOLIC REGULARIZATION | HEAT | SHEAR-FLOW | DIRECTION | CONVERGENCE | PERONA-MALIK EQUATION | MODEL | DIFFUSION EQUATION
Journal Article
2006, Oxford lecture series in mathematics and its applications, ISBN 0199202974, Volume 33, xiii, 234
This book is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the... 
Burgers equation | applied mathematics | Delayed regularity | Singular parabolicity | Smoothing | Nonlinearities of power type | Asymptotics | Extinction in finite time | Time decay | Decay rates | Classical heat equation
Book
Nonlinear Analysis, ISSN 0362-546X, 2010, Volume 73, Issue 11, pp. 3507 - 3512
The present paper is concerned with the blow up rate of a solution to the following Cauchy problem u t = Δ u m + u p , ( x , t ) ∈ R N × ( 0 , T ) , with the... 
Porous medium equation | Blow up rate | Cauchy problem | MATHEMATICS | MATHEMATICS, APPLIED | SEMILINEAR HEAT-EQUATIONS | Mathematical analysis | Images | Proving | Oscillations | Nonlinearity | Estimates
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 12/2012, Volume 53, Issue 12, p. 123515
Preliminary group classification became a prominent tool in the symmetry analysis of differential equations due to the paper by Ibragimov, Torrisi, and Valenti... 
HEAT | EIKONAL EQUATION | SYMMETRIES | PARTIAL-DIFFERENTIAL-EQUATIONS | DIFFUSION-EQUATIONS | ALGEBRA | POWER NONLINEARITIES | LIE | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | TRANSFORMATIONS | Algebra | Wave equations | Classification | Group theory | Differential equations | Nonlinearity | Transformations | Symmetry
Journal Article
Analysis and PDE, ISSN 2157-5045, 2013, Volume 6, Issue 7, pp. 1719 - 1754
We study the initial-boundary value problem {u(t) = Delta phi(u) + epsilon Delta[psi(u)](t) in Q := Omega x (0, T], phi(u) + epsilon[psi(u)](t) = 0 in partial... 
Bounded radon measures | Entropy inequalities | Pseudoparabolic regularization | Forward-backward parabolic equations | forward-backward parabolic equations | bounded radon measures | MATHEMATICS | HEAT | MATHEMATICS, APPLIED | SHEAR-FLOW | pseudoparabolic regularization | DIFFUSION | MODEL | entropy inequalities
Journal Article
Analysis, ISSN 0174-4747, 03/2018, Volume 38, Issue 1, pp. 21 - 36
The initial value problem for an inhomogeneous nonlinear heat equation with a pure power nonlinearity is investigated. In the radial energy space, global and... 
Nonlinear heat equation | global well-posedness | 35K55 | blow-up
Journal Article
Boundary Value Problems, ISSN 1687-2762, 12/2018, Volume 2018, Issue 1, pp. 1 - 11
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 03/2006, Volume 31, Issue 3, pp. 469 - 495
This article deals with a class of nonlinear elliptic equations involving a critical power-nonlinearity as well as a potential featuring multiple inverse... 
Critical sobolev exponent | Hardy inequality | Multi-singular potentials | Concentration compactness Principle | concentration compactness Principle | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | critical sobolev exponent | EXPONENTS | INEQUALITIES | multi-singular potentials | HEAT-EQUATION
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2008, Volume 68, Issue 3, pp. 461 - 484
Journal Article
SIAM Journal on Applied Mathematics, ISSN 0036-1399, 1/2010, Volume 70, Issue 7/8, pp. 3319 - 3341
Journal Article
Heat and Mass Transfer, ISSN 0947-7411, 3/2017, Volume 53, Issue 3, pp. 1037 - 1049
Journal Article
Potential Analysis, ISSN 0926-2601, 3/2017, Volume 46, Issue 3, pp. 589 - 608
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2006, Volume 358, Issue 3, pp. 1165 - 1185
We study large time asymptotics of small solutions to the Cauchy problem for nonlinear damped wave equations with a critical nonlinearity \begin{equation*}... 
Preliminary estimates | Damping | Heat equation | Wave equations | Nonlinearity | Fourier transformations | Mathematics | Cauchy problem | Damped wave equation | Large time asymptotics | MATHEMATICS | CRITICAL EXPONENT | GLOBAL EXISTENCE | DECAY | BEHAVIOR | damped wave equation | CAUCHY-PROBLEM | large time asymptotics
Journal Article
Journal of the Acoustical Society of America, ISSN 0001-4966, 09/2011, Volume 130, Issue 3, pp. 1125 - 1132
Journal Article
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, ISSN 0965-5425, 06/2019, Volume 59, Issue 6, pp. 1015 - 1029
Journal Article
Mathematical Problems in Engineering, ISSN 1024-123X, 2/2015, Volume 2015, pp. 1 - 7
We propose a power series extender method to obtain approximate solutions of nonlinear differential equations. In order to assess the benefits of this... 
MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | HOMOTOPY | HEAT-TRANSFER | Series | Research | Differential equations, Nonlinear | Mathematical research | Approximation | Perturbation methods | Mathematical analysis | Differential equations | Nonlinearity | Taylor series | Mathematical models | Power series | Convergence
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2009, Volume 71, Issue 5, pp. 2236 - 2256
We study the behavior of solutions of the Cauchy problem for a semilinear parabolic equation with a singular power nonlinearity. It is known for a... 
Singularity | Stationary solution | Critical exponent | Semilinear heat equation | Cauchy problem | Convergence | MATHEMATICS, APPLIED | CAUCHY-PROBLEM | ELLIPTIC EQUATION | SUPERCRITICAL NONLINEARITY | DIFFUSION EQUATION | GROW-UP RATE | MATHEMATICS | HEAT-EQUATION
Journal Article
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