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Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 1/2011, Volume 40, Issue 1, pp. 15 - 36
Journal Article
Mathematische Annalen, ISSN 0025-5831, 12/2015, Volume 363, Issue 3, pp. 1117 - 1145
We consider the maximal regularity problem for non-autonomous evolution equations 1 Each operator $$A(t)$$ A ( t ) is associated with a sesquilinear form... 
47D06 | Mathematics, general | Mathematics | 35K50 | 35K45 | 35K90 | MATHEMATICS | PARABOLIC EQUATIONS | PSEUDODIFFERENTIAL-OPERATORS
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 11/2019, Volume 119, Issue 5, pp. 1279 - 1335
This paper is concerned with some spreading properties of monostable Lotka–Volterra two‐species competition‐diffusion systems when the initial values are null... 
92D25 (primary) | 35K57 | 35K45 | Analysis of PDEs | Mathematics
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 06/2014, Volume 256, Issue 12, pp. 3912 - 3942
In this paper we introduce a purely variational approach to time dependent problems, yielding the existence of global parabolic minimizers, that... 
Parabolic minimizers | Parabolic systems | Evolutionary solutions via calculus of variations | Evolutionary variational solutions | Existence | 35D05 | 49J40 | 35A01 | 35K45 | 35K87 | PARABOLIC EQUATIONS | METRIC-SPACES | PRINCIPLE | GRADIENT FLOWS | CONJECTURE | MATHEMATICS | ENERGY-DISSIPATION FUNCTIONALS | GIORGI | GROWTH | SYSTEMS
Journal Article
Journal of Nonlinear Science, ISSN 0938-8974, 10/2011, Volume 21, Issue 5, pp. 747 - 783
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 04/2019, Volume 292, Issue 4, pp. 724 - 732
In this paper we consider a one‐dimensional fully parabolic quasilinear Keller–Segel system with critical nonlinear diffusion. We show uniform‐in‐time... 
boundedness of solutions | 92C17 | Lyapunov‐like functional | 35K45 | 35B45 | chemotaxis | Lyapunov-like functional | MATHEMATICS
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 7/2016, Volume 107, Issue 1, pp. 43 - 57
We consider a linear non-autonomous evolutionary Cauchy problem 0.1 $$\begin{aligned}\dot{u}(t)+{\mathcal{A}}(t)u(t)=f(t) \quad { for } \; {a.e. t} \in... 
47D06 | 35K50 | Approximation | Sesquilinear forms | 35K90 | Maximal regularity | Mathematics, general | Mathematics | Non-autonomous evolution equations | 35K45 | MATHEMATICS
Journal Article
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 04/2018, Volume 21, Issue 2, pp. 276 - 311
We discuss an initial-boundary value problem for a fractional diffusion equation with Caputo time-fractional derivative where the coefficients are dependent on... 
weak solution | Primary 35R11 | initial-boundary value problem | regularity | fractional diffusion equation | Secondary 35K45, 26A33, 34A08 | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SPACES | WEAK SOLUTIONS | Time dependence | Dirichlet problem | Boundary value problems
Journal Article
Journal of Mathematical Biology, ISSN 0303-6812, 5/2016, Volume 72, Issue 6, pp. 1429 - 1439
In this short paper, we establish a priori $$L^\infty $$ L ∞ -norm estimates for solutions of a class of reaction-diffusion systems which can be used to model... 
92D30 | Reaction-diffusion system | A priori $$L^\infty $$ L ∞ -norm estimate | Epidemic models | Mathematical and Computational Biology | 35B45 | Mathematics | Applications of Mathematics | 35K45
Journal Article
Journal of Evolution Equations, ISSN 1424-3199, 6/2018, Volume 18, Issue 2, pp. 755 - 775
We study the large time behavior of a class of diffusive predator–prey systems posed on the whole Euclidean space. By studying a family of similar problems... 
Persistence | Predator–prey system | Analysis | Asymptotic behavior | Mathematics | 35K57 | 35K45 | 35K55 | MATHEMATICS | MATHEMATICS, APPLIED | Predator-prey system
Journal Article
Osaka Journal of Mathematics, ISSN 0030-6126, 06/2012, Volume 49, Issue 2, pp. 331 - 348
Consider the Cauchy problem for a system of weakly coupled heat equations, whose typical one is {u(t) - Delta u = vertical bar v vertical bar(p-1)v, v(t) -... 
MATHEMATICS | CAUCHY-PROBLEM | NONEXISTENCE | BLOW-UP | GLOBAL EXISTENCE | 35K45 | 35B40
Journal Article
Stochastic Partial Differential Equations: Analysis and Computations, ISSN 2194-0401, 3/2015, Volume 3, Issue 1, pp. 52 - 83
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 7/2015, Volume 105, Issue 1, pp. 79 - 91
We consider the maximal regularity problem for non-autonomous evolution equations 0.1 $$\begin{array}{l}{u'(t) + A(t)\,u(t) = f(t), \quad t \in (0, \tau]}\\... 
47D06 | 35K50 | Sesquilinear forms | 35K90 | Maximal regularity | Mathematics, general | Mathematics | Non-autonomous evolution equations | 35K45 | Differential operators with boundary conditions | MATHEMATICS | Bisphenol-A | Analysis of PDEs
Journal Article
Journal of Evolution Equations, ISSN 1424-3199, 9/2017, Volume 17, Issue 3, pp. 883 - 907
We consider non-autonomous evolutionary problems of the form $$u' (t)+A(t)u(t) = f(t), \quad u(0) = u_{0},$$ u ′ ( t ) + A ( t ) u ( t ) = f ( t ) , u ( 0 ) =... 
47D06 | 35K50 | Analysis | Sesquilinear forms | 35K90 | Maximal regularity | Mathematics | Non-autonomous evolution equations | 35K45 | FORMS | MATHEMATICS | MATHEMATICS, APPLIED | BESOV | EVOLUTION-EQUATIONS | L-P | SOBOLEV
Journal Article
Ricerche di Matematica, ISSN 0035-5038, 6/2019, Volume 68, Issue 1, pp. 295 - 314
A predator–prey system involving cross-diffusion is obtained at the formal level as a singular limit of a four-species reaction–diffusion system, following the... 
Cross-diffusion equations | 35B25 | 35B36 | Turing patterns | Functional responses | Probability Theory and Stochastic Processes | Mathematics | 35K57 | 35K45 | 35Q92 | Geometry | Predator–prey equations | Algebra | 92D25 | Turing instability | Analysis | Numerical Analysis | Mathematics, general | MATHEMATICS | MATHEMATICS, APPLIED | Predator-prey equations | MUTUAL INTERFERENCE
Journal Article
Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 6/2018, Volume 25, Issue 3, pp. 1 - 39
We consider in this paper a microscopic model (that is, a system of three reaction–diffusion equations) incorporating the dynamics of handling and searching... 
Cross-diffusion equations | 35B25 | 35B36 | Turing patterns | Mathematics | 35K57 | 35K45 | 35Q92 | Predator–prey equations | 92D25 | Turing instability | Analysis | functional responses | DERIVATION | EXISTENCE | MATHEMATICS, APPLIED | EQUATIONS | MUTUAL INTERFERENCE | PATTERN-FORMATION | FAST REACTION LIMIT | CROSS-DIFFUSION | DISCRETE | DYNAMICS | Predator-prey equations
Journal Article
Numerische Mathematik, ISSN 0029-599X, 7/2015, Volume 130, Issue 3, pp. 541 - 566
We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme (based on backward differentiation... 
Mathematical Methods in Physics | 35B35 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | Mathematics, general | Mathematics | 65M12 | 35K45 | ATTRACTORS | MATHEMATICS, APPLIED | APPROXIMATION | BOUNDS
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 7/2013, Volume 47, Issue 3, pp. 611 - 665
Journal Article
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